Tyro was the daughter of Salmoneus and his first wife Alcidice. Her name may be linked to that of Tyrrhenus (which see) and so to tyrsis, 'tower', with reference to her father's kingship of Elis. (This word does not, pace Robert Graves, seem to be related to 'tyrant', which is strictly speaking the Doric equivalent, tyrannos, of coiranos, which in turn comes from cyros or cyrios and mean 'lord'.)
It seems less likely that Tyro's name comes from the tryo element meaning 'to wear out' that we considered for Triton and Amphitrite. The English word 'tyro', incidentally, meaning 'beginner' or 'novice', seems to have no relation at all to her name. It apparently derives from Latin tiro, 'military recruit'.
