Sir Kay is the son of Sir Hector, and the foster-brother of Arthur. He, along with Bedivere, is one of the earliest characters to appear associated with Arthur in the literary cycles, appearing in early Welsh poems such as the Welsh Triads and Culhwch ac Olwen. His name appears in a variety of forms in the various sources. In English he is Kay or Kai, in French romances the name is spelled Keu, and in Welsh, his name is Cei or Cai. These last forms, the earliest ones, give clue to the origin: Cai is a Welsh form of the Roman praenomen Gaius (see entry in next edition), also spelled Caius. The origin of this praenomen is uncertain, but it may be related to Latin gaudere ‘to rejoice’. So with this name we have seen names of Celtic origin (Arthur, Gawain, Guinevere), Germanic origin (), and Greek origin (Elaine, Hector), and now we’ve a name of Roman origin. (It won’t be the last!)
The name was never common, but it was used in England, particularly in areas with strong Welsh and Breton connections; Reaney & Wilson s.n. Kay mention one Britius filius Kay from 1199.
It is not clear to what extent the relationship between Kay/Cai/Keu etc. and Gaius/Caius was recognized medievally — i.e., the extent to which occurrences of Gaius can be taken as examples of the influence of Arthurian legends. In fact, the extent is probably very minimal, especially given other more likely routes to the name, such as the various minor New Testament characters, saints, or popes. In Italy — which is where our current single example comes from — the influence of Julius Caesar, Pliny the Elder, and Tacitus, all of whose praenomina were Gaius on the Renaissance likely contributed to the use of the name more than the Arthurian character.