I think that is something that just has to be accepted with these kinds of stories, but at least she seems to have altered the shape of her eyes, and her hair colour.
As she went missing for about two years, it is at least plausible that they wouldn't assume it was the same person even if they are very similar. He at least asks if she has lost her memory, as he would suppose, if she was who she is, that she would tell him who she really is if she hasn't lost her memory.