It’s a grand, elegant name in itself but I think it’s a big name to pull off. People will naturally think of Grand Duchess Anastasia and the animated movie. It has sad associations, particularly if you’re a royalist or sympathetic towards the Russian royal family. It may help if you do have Russian heritage though, I guess, as it would be more common over there and not so specifically associated with the Romanovs.
Also, the Anastasia Steele and 50 Shades of Grey associations makes it less appealing too.