Actually, if you want to get really technical, it’s エアリス, which is spelled Earisu in romaji. Japanese is less versatile than English in terms of the sounds that can be made with it, and there is that pesky rule that consonants almost always need to be accompanied by a vowel, so there are quite a few different ways it could be translated into our language.
The Su at the end can be translated as just an S. There is no Th in the Japanese language, but it’s not far enough removed from the original sound to be a wholly invalid translation, and it sounds alright in English.
The possibilities don’t end there. What’s normally translated as an R sound in romaji is the liquid consonant that can be used for L or R as the actual sound really is neither. An I sound also sounds like Ee in Japanese. The far more common name Elise would have been a valid translation too, and it’s possible that was supposed to actually be her name. Whether the translation staff misunderstood the liquid consonant, or wanted to give the character more of a fantasy-sounding name, Aeris/Aerith is what they went with though.
Regardless of how her name is pronounced, this up and coming voice actress now has a great role to add to her resume.