How old is she and is she used to her name? If she is just call her that and jazz it up or change it for a showname. If not I have alwaysed loved Jindilla or Xanadu (pro-nounced Zan-a-du). But like I said don't change it if she is like 5 or more or just come up with something with the same ring to it.
When I was little my dad would always tell me "snowmane stories" about a beautiful pure white arabian that would rescue a little girl that just happened to be me but in different scenarios. So snowmane will be my first horses name as long as its absoulutely pure white.. haha. Then for me comes sheherazade... you might have trouble pronouncing it but I find it to be a beautiful name for black horse again arabian horse because its an arabian name from the "Arabian Nights" then I would get a beautiful chestnut arabian that I would name sultan.... Ohh my gosh I have found myself dreaming about these three horses all my life... haha.... anyone intrested in giving a free horse to me???