Yes, I would, sorry. They don't really even sound that similar to me. It would be like using
Nicole as a nickname for
Natalia or something.
Anina is pretty, but the database says that it's a nickname for
Anna.
You could just call her
Anastasia, you know. Do Russians nickname everyone? Other ideas:
Ana,
Anna,
Anne,
Annie, Stasia,
Tasia, Sia...