I didn't name my Loftwing. Oddly, for as much as the game's NPCs stress the importance of Loftwings, I didn't really care about the bird. I cared about Epona, but not the bird with whom Link is supposed to hold a close bond. I think that had they shown a flashback of Link meeting his bird as a child, I might have cared. But, seeing as I didn't form a bond myself like in OoT, I just didn't care about it.
I'm hoping that team Himekawa gives it a name in their manga though. The way they draw the Loftwings is really cool and they look much more majestic than their game designs. ^_^