The original Hellenes were an ancient, probably Pelasgian, tribe of southern Thessaly and Phthiotis around and to the west of modern Lamia. Named after the mythical Hellen, son of Deucalion.
The designation Hellenic for a large number of tribes and cities of common ethnicity and religion is classical and definitely post-Homerian. As noted by Thucydides (who really wasn't buying the idea of a Hellenic nation) Homer named the Hellenes only as the followers of Achilles:
"Before the Trojan war there is no indication of any
common action in Hellas, nor indeed of the universal
prevalence of the name .... The best proof of this is
furnished by Homer. Born long after the Trojan War, he
nowhere calls all of them by that name, nor indeed any
of them except the followers of Achilles from Phthiotis,
who were the original Hellenes: in his poems they are
called Danaans, Argives, and Achaeans"
-- Thucydides: On The Early History of the Hellenes
Indeed, Homer refers neither to Hellenes nor to barbarians so the distinction probably didn't exist yet in the 7th century BCE. The first time the notion of Hellene vs barbarian takes the stage in history is during Xerxes' invasion of Greece in 480 BCE as part of a propaganda campaign by those cities who would resist the Persians aimed at gaining more allies. It became a mainstay during the times of the Macedonian king Philip II who used
the concept in part to legitimise his Macedonians as a Greek tribe, in part to unify the conquered cities of the south and his own divided people. Under the influence of Philip and his son, Alexander the Great, a Hellenic identity and culture was spread from the Ganges to Gibraltar.
Ironically, the Hellenic identity would give way to another one when the Byzantine emperors were trying to legitimise themselves as the true rulers of the Roman Empire. From the fourth century CE and until the 19th century, Greeks would refer to themselves as Romans. Only after the formation of the modern Greek state would term "Hellenic" rise to prominence again. In 1833 Otto I was crowned king of the Hellenes since it was not very practical to crown a king of the Romans who was not ruler of Rome (Charlemagne and the Byzantine emperors may have done it when Rome was in decline but the 19th century did not approve of it).
The figure of Hellen was probably just a rationalisation of the common heritage of the many different tribes and cities of ancient Greece. By way of his sons Dorus, Xuthus and Aeolus and their sons, Hellen became a common ancestor of all Greek tribes from the Ionian Sea to Asia Minor.