It's just faux-Russian to me. And changing the spelling of the name - especially if you're going to pronounce it anna-STAY-sha - to
Anastasiya is just wrong. The spelling screams out for the proper pronunciation of ana-STAS-ee-a.
I also really don't like "cute" middle names, since a name serves a purpose in life. I think something elegant is a better match.
My favorite combo is
Liv Anastasia - what about
Anastasia Liv?
Anya is a cute enough nn for
Anastasia, though.