Miniar and Ugla, both Icelandic members, should be able to shed more light on the subject and the laws regarding naming. I had the opportunity to visit Iceland three times, and know a couple of Icelanders outside of Susan's. As I recall, the Reykjavik telephone book was by first name.
One of my prized souvenirs from my visits there is a book by Freysteinn Johansson and Frederik Olfsson, entitled, Skakbok ab Fischer gegn Spassky.