Names of kings and cities in Genesis 14:2

The following is purely my speculation, I do not claim to know Hebrew or be a scholar.

Some of the names in the Bible are extremely symbolic and therefore possibly are not real names. No good parent would name their son "in wickedness." The names of the cities were likely given after the fact, we know this be the case with Zoar, as it is written:

Therefore the name of the city was called Zoar.--Genesis 19:22

Genesis 19 was when the cities were being destroyed and here we see the city Zoar being named because of the events of Genesis 19, yet this city is named much earlier in Genesis 13:10.  Perhaps, the other cities were likewise. If the cities were named (or renamed) perhaps the names of the kings in Genesis 14 were likewise?

Genesis 14:2 the kings of the cities God would later destroy were named:

they made war with Bera king of Sodom, and with Birsha king of Gomorrah, Shinab king of Admah, and Shemeber king of Zeboiim, and the king of Bela--the same is Zoar.--Genesis 14:2

עָשׂוּ מִלְחָמָה, אֶת-בֶּרַע מֶלֶךְ סְדֹם, וְאֶת-בִּרְשַׁע, מֶלֶךְ עֲמֹרָה; שִׁנְאָב מֶלֶךְ אַדְמָה, וְשֶׁמְאֵבֶר מֶלֶךְ צְבֹיִים, וּמֶלֶךְ בֶּלַע, הִיא-צֹעַר

They had an ally, the King of Salem, the city believed to be the future Jerusalem:

And Melchizedek king of Salem brought forth bread and wine; and he was priest of God the Most High. --Genesis 14:18

וּמַלְכִּי-צֶדֶק מֶלֶךְ שָׁלֵם, הוֹצִיא לֶחֶם וָיָיִן; וְהוּא כֹהֵן, לְאֵל עֶלְיוֹן

Bera--בֶּרַע
 Bera--בֶּרַע who is called King of Sodom, his name seems to mean "in evil", as it is used in Exodus 5:

And the officers of the children of Israel did see [that] they [were] in evil [בְּרָע --b'ra]  [case], after it was said, Ye shall not minish [ought] from your bricks of your daily task. --Exodus 5:19 KJV 1611

וַיִּרְאוּ שֹׁטְרֵי בְנֵי-יִשְׂרָאֵל, אֹתָם--בְּרָע לֵאמֹר:  לֹא-תִגְרְעוּ מִלִּבְנֵיכֶם, דְּבַר-יוֹם בְּיוֹמוֹ.

Genesis rabbah states:

....Rabbi Yehoshua ben Korḥa would [also] expound names. “Bera” – as he was a wicked son [ben ra]; --Genesis Rabbah 42

Midrash:

They made war against Bera because he was wicked [ra' רַע] in the sight of God [literally heaven] and man; --Midrash Tanchuma, Lech Lecha 8

עָשׂוּ מִלְחָמָה אֶת בֶּרַע, שֶׁהָיָה רַע לַשָּׁמַיִם וְלַבְּרִיּוֹת. --Midrash Tanchuma

Concerning the city of Sodom, prior to its destruction, the scriptures call it "evil" and "sinful" using the same root word that the king's name has--ra'.

and the men of Sodom are evil [ra'im רָעִים], and sinners before Jehovah exceedingly.--Genesis 13:13

וְאַנְשֵׁי סְדֹם, רָעִים וְחַטָּאִים, לַיהוָה, מְאֹד

Sodom סְדֹם

The name of Sodom סְדֹם s'dom is spelled the same as the Hebrew word for "their secret" or "their council," or "their deliberation." Modern Hebrew still uses the word sod to mean secret or mystery which is used in another context in Genesis.

Into their secret [b'sodam בְּסֹדָם], come not, O my soul! Unto their assembly be not united, O mine honour; For in their anger they slew a man, And in their self-will eradicated a prince.--Genesis 49:6 Young's Literal Translation

בְּסֹדָם אַל-תָּבֹא נַפְשִׁי, בִּקְהָלָם אַל-תֵּחַד כְּבֹדִי:  כִּי בְאַפָּם הָרְגוּ אִישׁ, וּבִרְצֹנָם עִקְּרוּ-שׁוֹר  

Perhaps referring to the sin of Sodomy? However, by the time they were destroyed according to Genesis 19 it was out in the open.

Strong's Concordance claims it can mean "burning" or "scorched," but I cannot find evidence for this claim.

Birsha בִּרְשַׁע

The next name, Birsha בִּרְשַׁע the king of Gomorrah, his name seems to mean "in wickedness" or "in iniquity" as it is used in Psalm 141 

Incline not my heart to an evil thing, To do habitually actions in wickedness [בְּרֶשַׁע b'resha] , With men working iniquity, Yea, I eat not of their pleasant things.--Psalm 141:4 Young's Literal Translation

אַל-תַּט-לִבִּי    לְדָבָר רָע,
לְהִתְעוֹלֵל עֲלִלוֹת    בְּרֶשַׁע--
אֶת-אִישִׁים    פֹּעֲלֵי-אָוֶן;
וּבַל-אֶלְחַם,    בְּמַנְעַמֵּיהֶם 

Genesis rabbah states:

“Birsha” – as he was an evil son [ben rasha]; --Genesis Rabbah 42

Midrash:

they made war upon Birsha because he had behaved evilly [רָשָׁע rasha]; --Midrash Tanchuma, Lech Lecha 8

בִּרְשַׁע, שֶׁנַּעֲשָׂה רָשָׁע. --Midrash Tanchuma, Lecha Lecha 8

 Gomorrah  עֲמֹרָה 

The city name Gomorrah  עֲמֹרָה most resembles the word 'omer עֹמֶר which is a Biblical unit for measuring grains, its roughly 3 liters of grains. 

This [is] the thing which the LORD hath commanded, Gather of it every man according to his eating, an omer [עֹמֶר] for every man, [according to] the number of your persons; take ye every man for [them] which [are] in his tents.--Exodus 16:16

זֶה הַדָּבָר, אֲשֶׁר צִוָּה יְהוָה, לִקְטוּ מִמֶּנּוּ, אִישׁ לְפִי אָכְלוֹ:  עֹמֶר לַגֻּלְגֹּלֶת, מִסְפַּר נַפְשֹׁתֵיכֶם--אִישׁ לַאֲשֶׁר בְּאָהֳלוֹ, תִּקָּחוּ

Maybe this alludes to them having lots of grains or food? Concerning the cities destroyed Ezekiel 16 states they had a lot of bread (which can be measured in omers)::

Behold, this was the iniquity of thy sister Sodom, pride, fulness of bread, and abundance of idleness was in her and in her daughters, neither did she strengthen the hand of the poor and needy.--Ezekiel 16:49

 We are told the cities of the plain were well watered so much so it was like the Garden of Eden, causing Lot to move there:

all the plain of the Jordan, that it was well watered every where, before the LORD destroyed Sodom and Gomorrah, like the garden of the LORD, like the land of Egypt, as thou goest unto Zoar. --Genesis 13:10

Part of the irony of the destruction of the cities was it went from water, rich soil, and fertile to fire scorched, soil and brimstone contaminated soil, and desolate. 

Perhaps, the city's name is portmanteau which means "disobedient people" or "rebellious people" since the word for "he rebels" is marah:

And when the prophet that brought him back from the way heard thereof, he said: 'It is the man of God, who rebelled [מָרָה marah] against the word of the LORD; therefore the LORD hath delivered him unto the lion, which hath torn him, and slain him, according to the word of the LORD, which He spoke unto him.--1 Kings 13:26

וַיִּשְׁמַע הַנָּבִיא, אֲשֶׁר הֱשִׁיבוֹ מִן-הַדֶּרֶךְ, וַיֹּאמֶר אִישׁ הָאֱלֹהִים הוּא, אֲשֶׁר מָרָה אֶת-פִּי יְהוָה; וַיִּתְּנֵהוּ יְהוָה לָאַרְיֵה, וַיִּשְׁבְּרֵהוּ וַיְמִתֵהוּ, כִּדְבַר יְהוָה, אֲשֶׁר דִּבֶּר-לוֹ 

 And they shall say unto the elders of his city, This our son [is] stubborn and rebellious [ וּמֹרֶה umoreh], he will not obey our voice; [he is] a glutton, and a drunkard.--Deuteronomy 21:20

וְאָמְרוּ אֶל-זִקְנֵי עִירוֹ, בְּנֵנוּ זֶה סוֹרֵר וּמֹרֶה--אֵינֶנּוּ שֹׁמֵעַ, בְּקֹלֵנוּ; זוֹלֵל, וְסֹבֵא

'am is a common Hebrew word for people

And the LORD said, Behold, the people [עַם 'am] [is] one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do.--Genesis 11:6

וַיֹּאמֶר יְהוָה, הֵן עַם אֶחָד וְשָׂפָה אַחַת לְכֻלָּם, וְזֶה, הַחִלָּם לַעֲשׂוֹת; וְעַתָּה לֹא-יִבָּצֵר מֵהֶם, כֹּל אֲשֶׁר יָזְמוּ לַעֲשׂוֹת 

Rebellious people would make sense because they their evil is rebellion against God, but Genesis 14:3 also says they rebelled against the king they were subjugated to for the last 12 years.

Though seemingly less likely, the word resembles a portmanteau of  'am (people) and marah (bitter), in Exodus 15:23 the place of Marah had 'bitter' water. 

Still more others suggest other names that I cannot check out like "submersion." 

Shinab שִׁנְאָב

Shinab שִׁנְאָב (shin'av) the king of Admah, his name seems to mean "hate father." The words are not used in any sentence together in the Hebrew Bible that I can find. The second half of the name seems obvious--Av אָב means father, as in: 

Neither shall thy name any more be called Abram, but thy name shall be Abraham; for a father [av אָב ] of many nations have I made thee.--Genesis 17:5

וְלֹא-יִקָּרֵא עוֹד אֶת-שִׁמְךָ, אַבְרָם; וְהָיָה שִׁמְךָ אַבְרָהָם, כִּי אַב-הֲמוֹן גּוֹיִם נְתַתִּיךָ

The first half is can be שִׁנְ shin which means "tooth" (Exodus 21:24 "eye for eye, tooth for tooth" or "ivory" (Amos 6:4) which considering the other names in Genesis 14 makes little sense. Or, it can be שִׁנְאָ which means "sleep" (Psalm 127:2) which also does not make a whole lot of sense. There is another option, though spelled slightly different in modern Hebrew lacking the dot on the topic right of the shin and having it instead on the top left making the letter called "sin", שָׂנֵא sana which means hate as in:

Neither will you set up a pillar, which the LORD you God hates [שָׂנֵא sana].--Deuteronomy 16:22

וְלֹא-תָקִים לְךָ, מַצֵּבָה, אֲשֶׁר שָׂנֵא, יְהוָה אֱלֹהֶיךָ. 

Since ancient Hebrew had the shin and sin written the same, and there were pretty much no diacritics at all, שָׂנֵא and שִׁנְאָ would be written the same--as שנא.  In this case, the name Shinav would "hates father." This could mean he hated his own father, or it could mean he hated God. Some like the Medieval French Rabbi Rashi claims this means he hated the heavenly Father. The name then probably means this king hated God.

Genesis Rabbah states:

“Shinav” – as he aspired [shoev] to wealth; --Genesis Rabbah 42

Midrash is in favor of "hates father":

they fought against Shinab because he detested [שׂוֹנֵא soné] the Heavenly Father [לָאָב la'av] ;--Midrash Tanchuma, Lech Lecha 8

שִׁנְאָב, שֶׁהָיָה שׂוֹנֵא לָאָב שֶׁבַּשָּׁמַיִם. -- Midrash Tanchuma Lech Lecha 8 

Admah אַדְמָה

The city's name was Admah אַדְמָה . The first man, as well as humanity in general, is called adam. However, words with the same spelling as Adam exist in scripture. Adamah mean soil, Adam's name refers to the fact he is spoken of as being made from dirt. The word can also mean red/brown like the color of soil. The word for blood is dam. The word for silence is dumah.

(Perfect match of letters): adamah אֲדָמָה --soil/ground here is an occurrence:

And she again bare his brother Abel. And Abel was a keeper of sheep, but Cain was a tiller of the ground [אֲדָמָה adamah]--Genesis 4:2

 וַתֹּסֶף לָלֶדֶת, אֶת-אָחִיו אֶת-הָבֶל; וַיְהִי-הֶבֶל, רֹעֵה צֹאן, וְקַיִן, הָיָה עֹבֵד אֲדָמָה

Perhaps the city is called "soil" or "earth" because it was fertile land as mentioned before.

(Close match): Adam אָדָם --adam or human, as in:

And the man [haadam הָאָדָם] gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam [וּלְאָדָם ul'adam] there was not found a help meet for him.--Genesis 2:20

וַיִּקְרָא הָאָדָם שֵׁמוֹת, לְכָל-הַבְּהֵמָה וּלְעוֹף הַשָּׁמַיִם, וּלְכֹל, חַיַּת הַשָּׂדֶה; וּלְאָדָם, לֹא-מָצָא עֵזֶר כְּנֶגְדּוֹ

Shemeber/shem'ever שֶׁמְאֵבֶר

The other Shemeber שֶׁמְאֵבֶר--is even less apparent. שֶׁמְ can mean "placing" שֶׂם  "sem" or "there" שָׁם as in "they got out of there," or "name" which in term can refer to authority, it is also the name of a son of Noah--Shem.

The word is used in the senses of "there" and "placing" is found in Genesis 2:

And the LORD God planted a garden eastward, in Eden; and there He put [וַיָּשֶׂם שָׁם vayysem sham] the man whom He had formed. --Genesis 2:8

 וַיִּטַּע יְהוָה אֱלֹהִים, גַּן-בְּעֵדֶן--מִקֶּדֶם; וַיָּשֶׂם שָׁם, אֶת-הָאָדָם אֲשֶׁר יָצָר.

The meaning of "name" is found in Genesis 2:

The name of [שָׁם sham] the first is Pishon; that is it which compasseth the whole land of Havilah, where there is gold;--Genesis 2:11

שֵׁם הָאֶחָד, פִּישׁוֹן--הוּא הַסֹּבֵב, אֵת כָּל-אֶרֶץ הַחֲוִילָה, אֲשֶׁר-שָׁם, הַזָּהָב.

Eber אֵבֶר (ever) means wings as in:

And I said: 'Oh that I had wings (אֵבֶר ever) like a dove! then would I fly away, and be at rest.--Psalm 55:6(7)

וָאֹמַר--מִי-יִתֶּן-לִי אֵבֶר, כַּיּוֹנָה:    אָעוּפָה וְאֶשְׁכֹּנָה

Shem being the name of Noah's son is found in Genesis also:

Now these are the generations of the sons of Noah: Shem (שֵׁם), Ham, and Japheth; and unto them were sons born after the flood.--Genesis 10:1

 וְאֵלֶּה תּוֹלְדֹת בְּנֵי-נֹחַ, שֵׁם חָם וָיָפֶת; וַיִּוָּלְדוּ לָהֶם בָּנִים, אַחַר הַמַּבּוּל 

Rashi claims it means to spring and rebel against God, but that seems like a stretch. Interestingly, there is tradition in the Early Christians and Jews that Shem is Melchizedek, if this is the case, perhaps its alluding to being an ally of Melchizedek--"Shem's wings"? 

Some suggest the shem part of the name is an abbreviated form of שמם which is often translated "desolation", as in:

He hath turned aside my ways, and pulled me in pieces: he hath made me desolate [שֹׁמֵם shomem].--Lamentations 3:11

 דְּרָכַי סוֹרֵר וַיְפַשְּׁחֵנִי, שָׂמַנִי שֹׁמֵם

The only issue would be one mem being dropped.

Still yet, there is another explanation that is offered from the Targum Pseudo-Jonathan:

Shemebar, who had corrupted himself with fornication,--Genesis 14:2 of the Jerusalem Targum (pseudo-Jonathan)

ושמאבר דמחבל איבריה ליזניה

 Where איבריה (translated corrupted) which members "limb" is understood as an euphemism for penis as it is used in later Jewish Babylonian Aramaic. 

So, the name can potentially (and absurdly) mean "desolate penis" or "Shen

Then Genesis Rabbah has:

“Shemever” – as he would fly off to bring wealth; --Genesis Rabbah 42

Midrash:

 Shemeber because he had said, “I will ascend with a wing [בָּאֵבֶר ba'aver] above the heights of the clouds.”  --Midrash Tanchuma, Lech Lecha 8

שֶׁמְאֵבֶר, שֶׁאָמַר אֶעֱלֶה בָּאֵבֶר עַל בָּמֳתֵי עָב. --Midrash Tanchuma, Lech Lecha 8

Zeboiim צְבֹיִים tz'voyim

The name of the city Zeboiim is spelled at least 4 ways in scripture: צְבֹיִים tz'voyim (1 variant of Genesis 14:2's spelling), צבויים tz'voyim (other variant of Genesis 14:2), צְבֹיִם tz'voyim (Genesis 10:19), צְבֹאיִם tz'voyim (Hosea 11:8).  The word exists in 5 verses: Genesis 10:19, Genesis 14:2, Genesis 14:8, Deuteronomy 29:23, Hosea 11:8.   

[Perfect match for Hosea 11:8 spelling] The spelling Hosea 11:8 spelling צְבֹאיִם is found again in Numbers 31:42, which might imply the city is named for fighting/war:

And of the children of Israel's half, which Moses divided off from the men that warred [הַצֹּבְאִים hatztzov'im]--Numbers 31:42

וּמִמַּחֲצִית, בְּנֵי יִשְׂרָאֵל, אֲשֶׁר חָצָה מֹשֶׁה, מִן-הָאֲנָשִׁים הַצֹּבְאִים.

This does matched Genesis 14 which is about war. The word refers to a gathering for the purposes of fighting/war and is derived from Tzva, which is part of God's titles, "LORD of Hosts" "YHVH tzvaot" where tz'vaot or Tz'va referring to armies. Here is an instance in which tz'vaot "hosts" or "armies" is used, along with the related word for fight tzi'bo.

For thus saith the LORD unto me: Like as the lion, or the young lion, growling over his prey, though a multitude of shepherds be called forth against him, will not be dismayed at their voice, nor abase himself for the noise of them; so will the LORD of hosts [צְבָאוֹת] come down to fight [לִצְבֹּא litz'bo] upon mount Zion, and upon the hill thereof. --Isaiah 31:4

כִּי כֹה אָמַר-יְהוָה אֵלַי כַּאֲשֶׁר יֶהְגֶּה הָאַרְיֵה וְהַכְּפִיר עַל-טַרְפּוֹ, אֲשֶׁר יִקָּרֵא עָלָיו מְלֹא רֹעִים, מִקּוֹלָם לֹא יֵחָת, וּמֵהֲמוֹנָם לֹא יַעֲנֶה; כֵּן, יֵרֵד יְהוָה צְבָאוֹת, לִצְבֹּא עַל-הַר-צִיּוֹן, וְעַל-גִּבְעָתָהּ

[Perfect match 1 Chronicles 12:9]: There is an animal mentioned a few times in scripture, whose identity is debated some say is a hyena, gazelle, or a deer. Here is an instance of a perfect match for tz'vayim]

And of the Gadites there separated themselves unto David to the stronghold in the wilderness, mighty men of valour, men trained for war, that could handle shield and spear; whose faces were like the faces of lions, and they were as swift as the roes [צְבָאיִם tz'vayim] upon the mountains; --1 Chronicles 12:9

וּמִן-הַגָּדִי נִבְדְּלוּ אֶל-דָּוִיד לַמְצַד מִדְבָּרָה גִּבֹּרֵי הַחַיִל, אַנְשֵׁי צָבָא לַמִּלְחָמָה--עֹרְכֵי צִנָּה, וָרֹמַח; וּפְנֵי אַרְיֵה פְּנֵיהֶם, וְכִצְבָאיִם עַל-הֶהָרִים לְמַהֵר.

Bela בֶּלַע

Next, the next mention is the city of Bela בֶּלַע  Bela' which we have a perfect match for spelling for too where it means "swallow", "devour":

He hath swallowed [בָּלַע bala'] down riches, and he shall vomit them up again; God shall cast them out of his belly.--Job 20:15

חַיִל בָּלַע, וַיְקִאֶנּוּ;    מִבִּטְנוֹ, יֹרִשֶׁנּוּ אֵל.

The root of the word is also found in Genesis 41:7--

And the seven thin ears devoured [וַתִּבְלַעְנָה] the seven rank and full ears. And Pharaoh awoke, and, behold, [it was] a dream.--Genesis 41:7

 וַתִּבְלַעְנָה, הַשִּׁבֳּלִים הַדַּקּוֹת, אֵת שֶׁבַע הַשִּׁבֳּלִים, הַבְּרִיאוֹת וְהַמְּלֵאוֹת; וַיִּיקַץ פַּרְעֹה, וְהִנֵּה חֲלוֹם.

The meaning "devoured" is confirmed in the Jewish targum pseudo-Jonathan:

the king of the city which consumed (Bela) the dwellers thereof, which is Zoar.  --Jerusalem Targum (pseudo Jonathan) Genesis 14:2

Likewise, Genesis Rabbah:

“and the king of Bela, which is Tzoar” – as its residents were swallowed up [nitbale’u]. --Genesis Rabbah 42

Zoar צֹעַר Tzo'ar

[Biblical explanation provided in scripture]: Finally, on the list of Genesis 14:2 we have the city of Zoar צֹעַר Tzo'ar, which is spelled צוֹעַר tzoar in 3 times in Genesis 19 (19:22, 19:30). The meaning of the name of the city of Tzo'ar is actually provided in Scripture, it was named after Genesis 19 because it was a little, insignificant, or young city that God did not rain fire and brimstone on, as we see:

Behold now, this city is near to flee unto, and it is a little one [מִצְעָר]; oh, let me escape thither--is it not a little one [מִצְעָר mitz'ar]?--and my soul shall live.' And he said unto him: 'See, I have accepted thee concerning this thing also, that I will not overthrow the city of which thou hast spoken. Hasten thou, escape thither; for I cannot do any thing till thou be come thither.'--Therefore the name of the city was called Zoar [צוֹעַר tzo'ar].--Genesis 19:20-22

הִנֵּה-נָא הָעִיר הַזֹּאת קְרֹבָה, לָנוּס שָׁמָּה--וְהִוא מִצְעָר; אִמָּלְטָה נָּא שָׁמָּה, הֲלֹא מִצְעָר הִוא--וּתְחִי נַפְשִׁי וַיֹּאמֶר אֵלָיו--הִנֵּה נָשָׂאתִי פָנֶיךָ, גַּם לַדָּבָר הַזֶּה:  לְבִלְתִּי הָפְכִּי אֶת-הָעִיר, אֲשֶׁר דִּבַּרְתָּ. מַהֵר, הִמָּלֵט שָׁמָּה, כִּי לֹא אוּכַל לַעֲשׂוֹת דָּבָר, עַד-בֹּאֲךָ שָׁמָּה; עַל-כֵּן קָרָא שֵׁם-הָעִיר, צוֹעַר. 

Then, you have another king named Righteous King, Melki-tzedek, king of Salem (serenity), a type of Christ according to the Letter to the Hebrews. Though Shalem is interpreted as serenity, the original meaning according to some refers to the Cannanite god of evening Shalem. It is interesting in the Code of Hamurrabi (dated 1750 BC), Hammurabi is called "king of righteousness." Perhaps this was a common title used by kings?

Probably not their birth names.