The name Caia is a girl's name meaning "to rejoice". Caia and is often added to lists like Best Cool Unusual Girls' Names and discussed in our forums with posts like "Totally, Kinda, or No Way?".
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.