One of my students at my school where I taught had the name Ai even though she used the kanji for "grace", which is usually pronounced "megu" or "megumi" on its own and "e" (ay) in names with other kanji present. This would be rather rare though.Some other Japanese names with Ai in them: Aiko AinaThe character for "ai" is pronounced "a" in some names and there are many names where this is used.
There is no set list of Japanese names, and many different kanji with many different meanings can have the same pronunciation. "Ai", for example, can mean "Asia clothes", with "a" meaning Asia, and "i" meaning clothes. This is not particularly common, though.
Some other Japanese names with Ai in them:
Aiko
Aina
The character for "ai" is pronounced "a" in some names and there are many names where this is used.