Unique names that don't confuse everybody in how they should be said or used (well, I slaughtered the pronunciation of Nuria but I don't care) I tend to like names of Spanish origin, I think because of Niño and his history.
I will NEVER re-use a name. I might name a child Layla, (my first dalmatian, motivated me to want to breed propper dals) or name a registered name kind of similar but I won't name them the same thing. I have Dizzy as a call name picked out and my horse's name was I'm A Player, so a horse name I have in mind is Dizzy Player. (I know )