Albina is also a Russian name as well as Italian. It isn't extremely popular, especially with girl's born now, but it was a fairly common name for girl's born in the 20's-40's.
I don't like "Al" or "Bean" or "Beanie" for a girl's nickname. "Albie" is ok but because this name is just way too close to the spelling for "albino", I couldn't ever saddle a child with it.