The name Caius is a boy's name of Latin origin meaning "rejoice". Caius and is often added to lists like Unique Boy Names: Unusual and Rare and discussed in our forums with posts like "Quick Question Thread?!".
From the experts:
Caius is classical and serious but also has a simple, joyful quality. There was a third century pope named Caius, as well as an early Christian writer, several Shakespearean characters, and a Twilight vampire. We would pronounce the name to rhyme with eye-us though at Cambridge University in England, where it's the name of a college, it's pronounced keys.
Caius is currently Number 164 on Nameberry.
Nickname Cai is a definite asset.