Icelandic name

Some family names do exist in Iceland, most commonly adaptations from last name patronyms Icelanders took up when living abroad, usually Denmark. Notable Icelanders who have an inherited family name include former prime minister Geir Haarde, football star Eiur Smari Gujohnsen, entrepreneur Magnus Scheving, film director Baltasar Kormakur Samper, actress Anita Briem and member of parliament (and former news reporter) Elin Hirst. Before 1925, it was legal to adopt new family names; one Icelander to do so was the Nobel Prize-winning author Halldor Laxness, while another author, Einar Hjorleifsson and his brothers all chose the family name ''Kvaran''. Since 1925, one cannot adopt a family name unless one explicitly has a legal right to do so through inheritance. (The law was amended in 1991 and 1996.)

Is this statement correct "do all last names in iceland end in son"?
no