I associate
Aida with the musical, and I often have heard it as eye-EE-dah. But I've also heard
Aida (on a Hispanic baby) prn. EYE-dah or EYE-ih-dah, almost. Both are pretty, but I do prefer
Ada (AY-dah). I probably wouldn't use the latter, though, due to the sudden overuse of the similar
Ava. :(