I've been doing a bit of personal research on the Greeks in southern Italy during the ancient period, and noticed quite quickly that it doesn't seem the Hellenes actually had a name for the region. While i know the Romans called it Magna Graecia due to the abundance of Greek colonists in the area, it seems odd that the Greeks never had a name for it. So did the ancient Greeks ever have a name for these parts of southern Italy? Or would they have just called it Megas Hellas, the Greek translated version of the roman name?
The Greek version of the term is “Megale Hellas”, but it’s not really clear if that’s what the Greeks actually called it, and therefore that Magna Graecia is a Latin translation of the Greek name; or, if the Romans called it Magna Graecia first, and later Greek authors translated the Latin into Greek. It’s possible that the Greeks didn’t have any particular term for their settlements in Italy, and also that if they did use the term “Megale Hellas”, it might have referred to any settlements in the Mediterranean, not just the Italian ones.
“The first absolutely ambiguous appearance of Magna Graecia in an Italian context is in Polybios, writing in the second century BC, but with reference to the sixth century. He described the exile of the Pythagoreans from many of the Greek colonies and the subsequent formation of the Italiote League, saying that the region of Italy in which these events took place was known as Megale Hellas.” (Lomas, pg. 8)
It's also not clear what exactly it refers to when it is used to refer to Italy. Some authors say it was just the southeast coast, some the entire south, some the south including Sicily. But whatever it was, and whether it was a contemporary term or not, the Greek term is certainly Megale Hellas.
Source: Kathryn Lomas, Rome and the Western Greeks, 350 BC - AD 200: Conquest and Acculturation in Southern Italy (Routledge, 1993)