The name Caius is a boy's name of Latin origin meaning "rejoice". Caius and is often added to lists like Cool Boy Names From Ancient Cultures and discussed in our forums with posts like "Picky Parents BNG".
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.