Ah, I'm horrible at names. But I've always liked the name Abigail (However the "proper" spelling is. I think I'd spell it weird anyway, like, Abygail.) But that's a person's name, so that won't do.
Hmm... Gynx would be a cool owl, I bet. She would be tawny with a smushed face, but very loving... when she wants to be, of course.
If I was a Mary-Sue (Merlin forbid) and I had an owl that liked ONLY ME and was a devil to everyone else I would name him/her Diablo. Yes, I did think of this during my early teenage years when I was angsty and wanted to be special. -_-
Otherwise, possibly Gwaihir or Thorondor or Landroval or Meneldor because I am a Lord of the Rings fangirl. Yes, I know those are the Eagles, not owls. And they would not appreciate their names being attached to a lowly owl. But still.