When I watched The Little Mermaid recently, a four-year-old girl picked it out. She didn't call the movie by its name; she said, "I want to watch Ariel".
This has happened to me before. I remember one little girl who told me she wants to watch Jasmine. Apparently, she doesn't know that Aladdin is the title character of the film. Then again, she can hardly be blamed for that. She's a little girl, and Disney markets Princess Jasmine to girls about a million times more often than they market Prince Aladdin to boys.
And this is part of the reason why I still think it was a bad decision to rename Rapunzel as Tangled. There is nothing wrong with naming the movie after the main character. In fact, it works much better than using a passive verb.
What alternate title could have been given to Frozen? The original title was The Snow Queen. Also, now that I've seen the movie...holy moly, the original preview was horrible and had nothing to do with anything.