Ἰναχείη, (Ἰναχιώνη), frequently occur as surnames of Io, the daughter of Inachus. (Verg. G. 3.153; Ov. Fast. 3.658, Met. 9.686; Aeschyl. Prom. 591; Callim. Hymn. in Dian. 254.) Epaphus, a grandson of Inachus, bears the same surname (Ov. Met. 1.753); and so also Perseus, merely because he was born at Argos, the city of Inachus. (Ov. Met. 4.719.)
[L.S]A Dictionary of Greek and Roman biography and mythology
Smith, William
A Dictionary of Greek and Roman biography and mythology. William Smith, LLD, ed. 1890