In the original ffvii psx english release her name was Aeris, and the pc port follows suit. This has been changed to Aerith in virtually every game she has been in since(KH,KH2,CC, etc.). So if you take a game as an individual work of art then her name is dependent on the game you are playing. If you see it as a series then her name is Aerith and she needs to have the s replaced with th when she joins your party in FFVII.