Gaius \gaius\ as a boy's name is of Latin origin, and the meaning of Gaius is "happy, rejoice". Probably the root of the word "gay", which used to mean "jolly". Also a biblical name, and the name of a Roman jurist in the second century. Caius is a variant that occurs in England.
Gaius has 7 variant forms: Cai, Caio, Kay, Kaye, Keye, Keyes and Keys.
For more information, see also the related name Jay.