I love Anna Sophia. Are you using it as a double-barrel first name. I love names like that...(like Mary Claire, Mary Kate, Anne Marie, etc..). The child actress is named AnnaSophia Robb. I like it better like Anna Sophia. AnnaSophia looks cramped and Anna Sophia looks clean and sophisticated. She was the actress in "Because of Winn-Dixie", "Bridge to Terabithia", and the new "Charlie and the Chocolate Factory".
I ADORE the name Anna, I think it is just about perfect. It sounds so heavenly to me.
I LOVE Anna Sophia. I wouldn't have assumed that you named her after the actress, they're two completely different spellings. And, like you said, Anna Sophia are two common names. I love it. I say go with it.