Help me, what is its name?

I believe it's called simply Cousin's Waltz. I believe it was composed by Angelo Badelimenti (not sure of the spelling on his name), the man who wrote the score for the film. It is a lovely piece of music. There are a couple of different versions on the soundtrack.

Oh, I see that in an earlier post the music has already been discussed in detail. If you look under the posting "The Music", you'll find more information.

Angelo Badalamenti