The original form of the Latin was not actually Graecus but Graius (plural Graei)--Graecus appears to be an expanded form imitating the Greek suffix "-kos." It appears that the name was taken from a Greek-speaking people bordering some Italian settlement and was later applied to the entirety of Greek-speakers (much the way that in Herodotus "Medes" generally refers to Persians and Iranian-speakers in general). The history of the term, though, is pretty uncertain and was confused even in antiquity. The Γραικοὶ were apparently a Thessalian people (like the Hellenes--Hellas was originally the term for an area of Thessaly on the river Spercheus) and were from an early date considered to be somehow related to the Hellenes, but how was never satisfactorily explained. A Byzantine scholar, quoting Hesiod, claims that original eponymous ancestor of Greek-speakers was not Hellen but a certain Graecus, whose brother was Latinus (contradicting a different tradition on Latinus' birth) and whose parents were Deucalion's daughter Pandora and Zeus. This would make Graecus Hellen's nephew, although another Byzantine scholar descends Graecus from Thessalus. Aristotle also says that originally the Hellenes were called Γραικοὶ, as does an inscription from the 4th Century. But ancient ethnographies are muddled at best, and these probably represent some sort of mythological connections that may or may not have any basis in reality and are probably not being fully understood by the authors mentioning them (Aristotle in particular seems to be thinking of the Graeci and Hellenes as being confined to Thessaly). In the historical period whoever these Thessalian Γραικοὶ were they had ceased to exist, although the Parians were called Γραῖκες and, being Aeolians, were possibly descended from this tribe. But none of this makes sense with the fact that the original Latin is Graius, not Graecus, and there appear not to be any Greek ethnic terms that lack the "-kos" ending and resemble Graecus. There are a few place names, but they don't seem to be related and are too far south. So basically the answer is...we don't really know. It used to be thought that when the Italians first encountered the Greeks back in the Archaic Period they were still known as Γραικοὶ (certainly Hellenes had not taken root yet) and that the word eventually was simply transmitted to Latin. But that doesn't seem to make much sense. The Romans must've got it from some small Greek tribe in Italy living next to an Italian people, but we don't know who they were or how the name was transmitted