Since the Greeks did not have standing armies, their armies did not have names. Their militias were simply referred to by their origin - "the Athenians", "the Corinthians". If a state sent out several expeditionary forces, they would generally be referred to by their commander's name, as in "the army of X" or "the men with X".

The only exception to this was the army of Greek mercenaries that marched with Cyrus the Younger against the King of Persia in 401 BC. These men were known to contemporary Greeks as the Cyreans. Later tradition has given them their more famous name - the Ten Thousand.

Some smaller units did have names. The Spartans had a royal bodyguard of 300 men called the hippeis (the name means "horsemen", but they fought on foot). The Argives had a corps of picked troops referred to simply as The Thousand. The Thebans had a similar unit, 300 strong, which Xenophon simply calls hoi epilektoi ("the picked men"), but which later sources insist were known as the hieros lochos, the Sacred Band. The Arkadians raised a standing force of five thousand men which they called the eparitoi - an Arkadian term of which the meaning is unknown.

Most of these units are rarely attested and short-lived. To my knowledge, no Greek unit was ever numbered, like Roman legions were.