Why Ana? They'll spend their lives telling people "No, it's only one N".
Because it's pronounced differently, presumably.
I like all three names, OP, but I think I would choose Anna. Annie doesn't seem quite substantial enough for someone's official name somehow, and although I really like Anne for people my age and older, I don't think its time has quite come for revival yet - you would get a lot of "oh, haven't heard that one in a long time, who is she named after?"