What is old name of Greece?

Hellas. That is what the Greeks called it, and they called themselves Hellenes (after their traditional founder Hellen. The word is still in use today). The word Greek arose when the Romans were penetrating the Italian peninsula. They ran into a tribe called the Graeci, then the Hellenes who had established city-states in southern Italy (Naples, Tarentum, Croton, Sybaris etc). Thinking them to be Graeci, they called the area Great Graeci. The name stuck.