And the winner is (dramatic pause...) Lilac!
My daughter carefully considered all the names suggested (thanks!) and did some very scientific experiments which involved calling her to see which one she responded to best. Okay then, Lilac it is!
She's doing great! She's starting to get the idea that she'll get a little chicken-flavored dog treat if she goes to the bathroom outside, instead of on the rug by the stairs, so that's progress.