Traditional naming customs of Iceland differ in that they follow no family lineage. Men are named after their father. I.e. If Jon has a son named Olaf, his name is Olaf Jonsson. If Olaf then has a son named Magnus, his name is Magnus Olafsson. It is not uncommon to go back and forth between two names. E.g. Olaf Jonsson might name his son Jon Olafsson, who would name his son Olaf. Women are similar with the suffix ‘dottir’.