Her name is pronounced Aeris so it only makes sense it should be spelled that way. Do you go around calling Sephiroth "Sephiros"? Because the rule applies to his name. Sephiroth, unlike sephiros, is actually a word. Look it up. Taking your cue from that, you should be able to figure out what's going on with Aeris' name. I don't care that they "corrected" it for the Advent Children credits. It doesn't make sense to spell it with a TH.

If Sephiroth = Sephiros,
Cloud Strife = Clutz Trifle
Tifa = Typhoid
Barret = Ballet
Cait Sith = Kite Zit
and
Cid = Seat