It is perfectly normal in Iceland that no two members of a family of four have the same surname, even though the parents are married. Children’s surnames are taken from their parents, most often the father’s name (i.e. a patronymic), but the family members do not all have a common family name as is generally the case in other countries. When an Icelandic child is born, it does not take on its father’s surname but rather his given name. The name of the child’s father (or mother) is given the suffix -son (son) or -dóttir (daughter) depending on the child’s gender. Certainly, there are family names in Iceland but they are unusual.
We can consider the following example of the names in an Icelandic family of four:
The father’s name is Guðmundur Sigurðsson and the mother’s name is Guðrún Þorvaldsdóttir. It is common for children to be named after their maternal or paternal grandparents. As such, the son might be called Þorvaldur Guðmundsson or Sigurður Guðmundsson. The daughter might bear the name of her father’s or mother’s mother, if custom was observed. In the case of her paternal grandmother’s name being Þórunn, and that her grandchild being named after her, she would be called Þórunn and be Guðmundsdóttir, that is, the daughter of Guðmundur. In this example, the father’s surname is Sigurðsson, the mother’s Þorvaldsdóttir, the son’s is Guðmundsson, and the daughter’s surname is Guðmundsdóttir.Given names are always used in preference to patronymic names or family names. One speaks about Guðmundur and Guðrún, not of Sigurðsson and Þorvaldsdóttir. A foreigner coming to Iceland who knew the Icelander Guðrún Þorvaldsdóttir and wanted to call her would look her up under her given name in the phone directory. There is one phone books covering the entire country, divided into categories after areas. Names are listed in alphabetical order according to given names, with the patronymic or surname coming after.