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In the short novel "The Lottery in Babylon", Jorge Luis Borges describes an imaginary society where a Lottery decides the fate of the people, with omnipotence and foresight. At the beginning of the original text we read

[ES] Miren: por este desgarrón de la capa se ve en mi estómago un tatuaje bermejo: es el segundo símbolo, Beth. Esta letra, en las noches de luna llena, me confiere poder sobre los hombres cuya marca es Ghimel, pero me subordina a los de Aleph, que en las noches sin luna deben obediencia a los Ghimel.

and in English:

[EN] Look: through this rent cape can be seen on my stomach a ruddy tattoo — it is the second symbol, Beth. On nights when the moon is full, this symbol confers unto me power over the men whose mark is Ghimel while rendering me subject to the men of Aleph, who on moonless nights must obey the men of Ghimel.

Since I first read this novel, I have been convinced that the sequence "aleph, beth, gimel" is the beginning of the Hebrew alphabet. Now I'm not sure any more, as the second letter is called "Bet", not "Beth".

So, if not Hebrew, what is the alphabet that the proconsul in Babylon is referring to?

"Bet" and "beth" are both valid spellings in Latin alphabet for the name of the letter "ב"; others include "beyt", "beh", "beis". The choice of the end sound comes from the type of Hebrew pronunciation used: "-t" is modern Israeli, "-th" is (academic) Tiberian pronunciation, and "-s" is an Ashkenazi pronunciation.

In modern Hebrew, it is also often pronounced with "v-" (as the letters ב and בּ without and with dagesh are distinguished, the one without dagesh being /v/ whereas the one with dagesh being /b/).

However, it was Imperial Aramaic that was the dominant language and script across the Neo-Assyrian, Neo-Babylonian and Achamenid empires that ruled over Babylon after 900 BCE. It employed and adapted the Phoenician script, so the Imperial Aramaic alphabet followed the same pattern, ordering and naming, as its relative the Hebrew script.

It is Hebrew. Hebrew letters have Hebrew names, written in Hebrew. Our transliteration into Latin alphabet is a convention and those can change, different authors may use different conventions for different reasons. The same word can be spelt differently in academic paper, high school textbook or online forum.

As others have said, it's Hebrew.

In academic/formal/archaic/Tiberian pronunciation, six of the Hebrew phonemes /b g d k p t/ can be realized in two different ways. When between vowels and not doubled, or at the end of the word, they're pronounced as fricatives and conventionally transcribed as bh gh dh kh ph th. When anywhere else, they're pronounced as stops and conventionally transcribed as b g d k p t.

Nowadays, in actual living/spoken Hebrew, some of these distinctions have vanished. The fricative versions of g d t are gone, and the fricative versions of b p are conventionally written as v f instead of bh ph. So the names of the first few Hebrew letters alphabet are now transcribed alef bet gimel dalet instead of aleph beth gimel daleth.

But Borges here is using the archaic spelling…mostly. You've probably also noticed ghimel, which is nowadays written as gimel. The /g/ comes at the beginning of a word, so it should be a stop, right?

Well, it is (and always has been) in Hebrew—but in Romance languages, people are used to gi being pronounced as in "genie" or "gin", not as in "gill" or "get". So Borges is using an Italian convention there, to spell the stop [g] as gh before the letters i and e.

P.S. Fricative gh and dh are pretty much gone for good, but th has left some traces: Israelis pronounce it [t], but Ashkenazim pronounce it [s]. So the word for "house" is now beit to Israelis but beis to Ashkenazim: that shows that it used to be beith. Some Sephardim also keep the fricatives, along with other archaic features like ŋayin.

P.P.S. Academics (generally those who aren't specifically studying Hebrew) also tend to use the old spellings that Borges uses here. That's why mathematicians talking about infinities will write aleph, beth, and so on.