Sony Computer Entertainment America fumbled the English Translation of FFVII and Aerith is one of the many, many things they got wrong.
(e) - (a) - (ri) - (su) is the name in Japanese Katakana. "Su" is a common replacement for "th", which doesn't exist in Japanese.
Aeris is a translation at face value by just looking at the Katakana. Aerith is a translation of intent, her name being a play on the English word "earth".
In every Square (Enix) translated game or media she's been corrected to Aerith. This includes Kingdom Hearts I & II, Crisis Core, Before Crisis, Advent Children, and the like.
The correct name is Aerith. But it's pronounced the same way as Aeris.
I always called her Aeris since I don't like Aerith at all.