Old English Grecas, Crecas (plural), early Germanic borrowing from Latin Graeci "the Hellenes," from Greek Grakoi. Aristotle, who was the first to use Graikhos as equivalent to Hellenes ("Meteorologica" I.xiv), wrote that it was the name originally used by Illyrians for the Dorians in Epirus, from Graii, native name of the people of Epirus.
But a modern theory (put forth by German classical historian Georg Busolt, 1850-1920), derives it from Graikhos "inhabitant of Graia" (literally "gray"), a town on the coast of Boeotia, which was the name given by the Romans to all Greeks, originally to the Greek colonists from Graia who helped found Cumae (9c. B.C.E.), the important city in southern Italy where the Latins first encountered Greeks. Under this theory, it was reborrowed in this general sense by the Greeks.
The Germanic languages originally borrowed the word with an initial -k- sound (cf. Old High German Chrech, Gothic Kreks), which probably was their initial sound closest to the Latin -g- at the time; the word was later refashioned.
Meaning "the Greek language" is from late 14c.; meaning "unintelligible speech, gibberish" is from c.1600. Meaning "Greek letter fraternity member" is student slang, 1900.