Icelandic Name Generator

Most Icelanders use a patronymic rather than a surname: the father's first name in the genitive plus -son for a son or -dóttir for a daughter. So Guðmundur's son Einar is Einar Guðmundsson and his daughter Helga is Helga Guðmundsdóttir. Women keep their own name at marriage, and children can instead take a matronymic from their mother, such as Helgudóttir or Kristínarson.

For women: Guðrún, Anna, Kristín, Sigríður, Margrét, Helga, Sigrún, Ingibjörg, Jóhanna and María. For men: Jón, Sigurður, Guðmundur, Gunnar, Ólafur, Einar, Kristján, Magnús, Stefán and Jóhann. The most common patronymics follow from those: Jónsdóttir, Sigurðardóttir, Guðmundsdóttir, Jónsson, Sigurðsson and Guðmundsson.

A few dozen survive, mostly adopted in the 18th and 19th centuries and now protected for existing families only: Blöndal, Briem, Thoroddsen, Nordal, Kvaran, Zoëga, Thorlacius, Hjaltalín, Schram, Möller, Thorarensen and Bergmann among them. New family names cannot be created, so they signal an old or prominent family.

Yes. Modern Icelandic is the closest living language to Old Norse, so names like Þorsteinn, Hrafn, Ketill, Ingibjörg and Þórdís are also authentic saga-era names, and the -son and -dóttir patronymics were used by the Vikings too. For a medieval feel favour the older stock (Grettir, Njáll, Skarphéðinn, Hallgerður) and avoid clearly modern imports like Viktor or Karen.