The name Caia is a girl's name meaning "to rejoice". Caia and is often added to lists like Unique Girl Names: Unusual and Rare and discussed in our forums with posts like "Heaven Hell Purgatory - Unusual/Outlandish Girls".
From the experts:
Caia Caecilia was the Roman Goddess of fire and women. The name Caia would make a truly fresh alternative to the flagging Maya, with which it rhymes.