From the experts:
Rapunzel is famous as the long-haired heroine of the fairy tale, locked in a tower only to fall in love with a handsome prince who climbed to her side via her hair. Rapunzel has never been widely used as a first name the way, say, Aurora -- the mortal name of Sleeping Beauty -- has. Like Cinderella, it's too closely identified with the fairy tale to really take off as a girls' name. And it's not the loveliest sounding girls' name either. Love Rapunzel the story, but the girls' name, not so much.