For The Last Time, Her Name Is Not Aerith

Her Japanese name is "Aerisu". There is no 'th' sound in Japanese. There is also no 'l' sound in Japanese, so just mentally substitute an 'l' for the 'r' there. "Aelisu".

Calling her "Alice" is more accurate than "Aerith", and you actually have no basis for the "Aerith" name - not in either version of the FFs, not in any other game, not, in fact, anywhere other than your own heads.

It just sort of bothers me.