Icelandic last names are patronymics: If Jóhann has a son named Leif and a daughter named Helga, the children's full names will be Leif Jóhannsson and Helga Jóhannsdóttir. (And if Leif has a daughter Þórdís, her full name will be Þórdís Leifsdóttir.) But because these aren't actual surnames—and because Iceland's population is relatively small and localized—first, not last, names dominate public life: Icelandic telephone directories are ordered by first name, and public figures are generally identified by first name in the press. Davíð Oddsson, who heads Iceland's Central Bank, would never be referred to as "Oddsson" alone—if a concise form of his name were needed, he'd be called "Davíð."

There are exceptions, of course. Some Icelanders have actual family names, passed unchanged from parent to child. These often date from before 1925, when it was legal to claim a family name by preference. In other cases, Icelanders have inherited a surname from a non-Icelandic ancestor. (This is the case for the prime minister, Geir Haarde: Haarde is Norwegian.) And sometimes last names are bestowed by a matronymic system instead. One of Iceland's soccer stars is Heiðar Helguson, whose name comes from Helga, his mother.