The Greek theory of the origin of the name Italy and three other hypotheses
One theory of the origin of the word “Italia” holds that the peninsula was originally named by the Greeks. Legend traces the name to the figure of Italus, grandson of Ulysses and king of the Oenotrians, Arcadian colonists who settled in what is now Calabria, on the western tip of the “boot”.
The region is thought to have acquired the name Italia later, and its Greek inhabitants the name Italiotes. In antiquity the name came to denote the whole peninsula as far as the Alps.
Everyone liked the name Italia so much that during the Social War the breakaway Italic confederation placed its capital at Corfinium, renamed it Italica, and issued a coin inscribed “Italia”.
The Greek theory, however, is only one of four principal etymological hypotheses; the others are: Italia as the land of Vitulus, an Etruscan origin, and an Oscan origin.
Still, the word “Greece” is of Roman origin, which only makes the story more tangled.