I checked, it's hard to tell. Greek didn't have the same exact alphabet than us, to begin with. And I'm not good enough in Greek for sure

French use "Alpha" (I'm french, I know). So does the brits. I wouldn't be surprised if it's because of William the (a lot of English have old French roots).
As for star charts, the arabs one come from the Abbassid, which predate the Turks. The Turks didn't (and still don't) speak an Arab language, they speak a language with roots in the north Asia, with mongols and stuff. Where they come from (they are relatively late invader of this region of the world).
In any case, the proper way to spell Alpha is άλφα. Everything else is not the proper way, and we deal with it.
The game use the NATO alphabet, and it's alfa. Also, it's Juliett, which is neither the proper French (Juliette) nor the proper English (Juliet) for it.