To be honest, there's a
Tiara at my school and I don't even register that it's the word for crown when I hear it. I used to think it was just some variant of
Tiana or some Latin-derived name that just happened to sound like a word in English. It follows the same patterns of the name
Chiara, so that might be part of it.
I think
Anya goes well with it. I don't think the movie is really a problem here.