Definitely do NOT ever consider giving the name "Andersen" to a girl, please.
I know it's very trendy these days to give surnames as first names to girls, but I really draw the line at any name that means "son of so-and-so" for a girl. And "Andersen" means "son of Andrew".
I don't think that Andersdottir ("daughter of Andrew") would make a cool name for a girl, either.
For a boy, I prefer simply "Ander" as a first name. I mean, if the boys' father isn't named "Andrew", then giving the kid a name that means "son of Andrew" might raise a few eyebrows. (As well as possibly raise the need for a DNA paternity test).