Why do they call Greece Greece?

Answer 1

The Greeks called and still call themselves Hellenes.

They overpopulated their small and poor country, and the city states sent out their surplus populations into colonies around the Mediterranean and Black Seas. Some colonies were established in Italy (Naples = Nea Polis, new city, Tarentum, Sybaris, Croton etc plus plenty in Sicily).

In their expansion down the Italian Peninsula in the 4th and 3rd Centuries BCE, the Romans encountered a Latin tribe called the Graeci. As they went further they ran into the Greek cities at the bottom of Italy, and thinking them to be a lot more of the Graeci tribe, called them the Magna Graeci.

The word Graeci (anglicised to 'Greek') was erroneously extended to the home country and people of the widespread Hellenic colonies, and the word Greek has stuck.