The answer is that the coin doesn't just say "Athens", but "of the Athenians" (ΑΘΕΝΑΙΟΝ). This word is abbreviated to just ΑΘΕ on the coins.

The vowel "eta" was originally not a part of the Classical Attic alphabet, at least not as a vowel. The letter "eta" in most Greek alphabets originally designated the aspirate, except in a few dialects like Ionian that didn't have an aspirate. The letter was used in Ionian fairly early in the Archaic Period to designate long vowels, which in Classical alphabets were not designated at all. Originally in Classical alphabets all vowels were marked by what would later become their short forms. So all the "e's" were marked by "epsilon," and all the "o's" were marked by "omicron." The Ionians started using "eta" to mark long vowels, first to mark long alphas, but when the long alpha merged in certain forms of Ionian into a long e the letter "eta" became used solely for the long e. In 403, just after the Peloponnesian War, the Athenians, whose dialect had close ties with the Ionian dialect, officially changed the alphabet so that "eta" no longer marked an aspirate but instead a long e, even though the Attic dialect still preserved an aspirate (in the Hellenistic Period this was solved by the use of the soft and hard breathing diacritical marks, which didn't exist until they were invented by the Alexandrian scholars). Later on the letter omega was added to the alphabet.

So technically it very well could stand for Athens, since the word was not spelled with an eta until much later. However, as /u/Smackaroo correctly points out, it doesn't. Greek and Roman coins, following the model of the Lydians (who invented coinage), did not write the city's or minter's name directly on the coin. Instead, since the coin represented the direct property of the person or state that had minted it, you stuck a genitive on their to indicate the possession. So, we usually find on Roman coins a nice long list of Imperial titles all in the genitive, to indicate that that coin is the property of whichever emperor or official had it minted. Same with this. That mark stands for athenaion, the genitive plural of ΆΘΗΝΑΙΟΣ (rendered in its Classical spelling as ΑΘΕΝΑΙΟΣ--I use all capitals because Greek only had capitals in the Classical Period), which would be ΆΘΗΝΑΙΩΝ (in its Classical spelling, ΑΘΕΝΑΙΟΝ--note the lack of the letters eta and omega)