I pronounce it an-a-STAY-zha. I think it's a nice name. I highly doubt many people will associate it with 50 Shades of
Gray. It's not a cultural phenomenon or anything to which names would be highly tied.
Lily Anastasia is a gorgeous combo.
Anya is an ok nickname, but it sounds forced to me unless maybe you had Russian or Eastern European ties. I have a friend
Anastasia who goes by Stasi (prn. like
Stacy). I like
Stacy as a nickname the best.