Many Icelandic names consist of a first name and a matronymic or patronymic, not a family name:
Björk Guðmundsdóttir (that is, Björk, Guðmund’s daughter)
Gunnar Karlsson (or Gunnar, son of Karl)
In a nonspecialist context, reverse the names in the works-cited-list entry:
Karlsson, Gunnar. The History of Iceland. U of Minnesota P, 2000.
The corresponding works-cited-list entry would thus use the matronymic or patronymic to key the in-text citation to the entry:
Another practice, followed by the Scandinavian Studies journal and suitable for book-length specialist works like those in Icelandic studies, is to begin the entry with the first name:
Gunnar Karlsson. The History of Iceland. U of Minnesota P, 2000.
Note that no comma is used between the first name and the patronymic because the elements of the name are not inverted.
The in-text reference thus uses the first name as the key to the entry: