What a charming, delightful, beautiful, and eye-catching name! I like it when Anne and Marie combined and formed this name. I like that it's a double name.
What a beautiful combination, though I do prefer Annaliese Marie, Anne could be a nickname and Marie is the middle. Simply the child can call herself Anne Marie.
I like this name a lot, not because of the singer. Though I think it would be less stress for the child to have Anne as a first name and Marie as a middle name.