One problem with this sentence is that the answer will be the same no matter which antecedent in chosen. If the girl's name is Mary; "name" = Mary, and "girl" = Mary. The name you want to know is the same as the name of the girl you want to know.
What is the name of the girl you want to know? => Mary (regardless of antecedent)
I think the question now has three tricks in it.