Iceland teen known legally as 'girl' fights for right to name

[KungKras]

But it was used to name a female character in litterature, right?

EDIT: Do the icelandic naming system work like most of the world with family names? Or do you do it like the vikings where if the father is named, say Björn, his son's last name will be Björnsson or if a mother's name is Tyra, the daughters last name will be Tyrasdotter?