The name Gaius is a boy's name of Latin origin meaning "to rejoice". Gaius and is often added to lists like Bible Names for Boys and discussed in our forums with posts like "Heaven, Hell, Purgatory - Boys".
From the experts:
Ancient Latin names are beginning to form a minitrend -- Marcellus, Aurelius, Augustus, Atticus, Magnus, Darius -- and this would certainly fit into that category. But though Gaius is pronounced guy-us, the teasing potential of the first syllable could be tough on a little boy.