In Greek mythology, Eleius (Ancient Greek: Ἠλεῖος) was son of Poseidon and Eurycyda daughter of Endymion. When his uncle Aetolus went into exile, Eleius became king of the Epeans, renamed his people the Eleans after himself, and gave the land the name Elis. He was the father of Augeas.
Adapted from Wikipedia, "Eleius" · CC BY-SA 4.0
I.Eponym of Elis
Pausanias sets Eleius in the Elean royal stem after Pelops. When Pelops' sons were scattered over the rest of the Peloponnese, the kingdom of the Epeans fell to Eleius son of Eurycyda daughter of Endymion — and, believe the tale who will, of Poseidon — who gave the inhabitants their present name of Eleans in place of Epeans (Description of Greece 5.1.8–9). The land was accordingly named Elis.
II.Augeas
His son Augeas succeeded him as king of Elis. Pausanias treats divine parentage as a glorifying play on a human name: those who exaggerate Augeas' glory give the name a turn and make Helius the Sun his father instead — yet the sober Elean account keeps Augeas son of Eleius, the eponym of Elis (5.1.9).
III.Homonyms
This atlas entry (eleius-elis) is the eponymous king, son of Eurycyda (and Poseidon). Distinct from a later Eleius in the same stem — descendant via Augeas, Agasthenes, Polyxenus, and Amphimachus — who ruled when the Heracleidae attempted their return; and from a son of Tantalus sometimes named as another possible eponym of Elis.