Elai was found as a baby somewhere near Onokoro; she was raised in the Ruby Sea area and then Kugane. She was named Elladie Byrne by the male Highlander who originally found her. She went to Eorzea - not out of choice really - when her Echo first started to show itself, and she was at Carteneau when Dalamud broke open. She renamed herself afterwards since no one remembered Elladie Byrne (head canon explanation for a race change after HW that included a name change, but Elladie is the character I played in 1.0). She picked a name she thought sounded vaguely Auri without really knowing much at all about her birth people