Old English Grecas, Crecas (plural) "Greeks, inhabitants of Greece," early Germanic borrowing from Latin Graeci "the Hellenes," apparently from Greek Graikoi. 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," also "old, withered"), 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 (compare 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. From late 14c. as "the Greek language." Meaning "unintelligible speech, gibberish, any language of which one is ignorant" is from c. 1600. Meaning "member of a Greek-letter fraternity" is student slang, 1884.
It was subtle of God to learn Greek when he wished to become an author -- and not to learn it better. [Nietzsche, "Beyond Good and Evil," 1886]