"Hellenic" is one of the original Greek words for "Greek". By Plato's time, it had become the standard name for this people. It is first found in Homer's Iliad, where it refers to the population of a small sub-region of Thessaly; Homer mainly uses other words to indicate the Greeks, such as Achaians, Argives, or Danaans. However, later on these other terms disappear and "Hellenes" becomes universal. The Greeks told tales of a mythical figure named Hellen, a descendant of Zeus, who was the ultimate ancestor of all Greek tribes. Modern Greeks now refer to their country as Hellas and to themselves as Hellênes.

The word "Greek" derives from the Latin name for Greeks (Graeci). This was originally used to designate the people from the town of Graia, in Boiotia (Central Greece), who had provided the lion's share of the settlers of Neapolis (modern Naples) in Southern Italy. When the Romans first encountered Greek-speaking people, these either identified themselves as, or were disparagingly dismissed as, Graioi or Graikoi. From this we get the modern word "Greek" in many Western languages. Plato would not have used it, however, because it was a foreign word for his people; he was no more inclined to refer to the Greeks by their Latin name than their Persian name (Yauna).

There are alternative traditions on each of these names and their origins; unfortunately, the Ancient Greeks themselves did not have a very clear picture of their own early history, and rival stories circulated even among the most learned scholars. But if the above it right, both terms date to the early Archaic period (8th-7th century BC).