Please, note that we attempt to collect surnames that trace their origin to Iceland and Iceland, as well as the names found there in the present days.
Having said all that we must notice here that in reality very few people in Iceland have surnames. What!? Yes, they mostly have their first names, second names and then in place of the surname, the majority of the people have a patronymic name. That is right, they just take, say, their father's first name, add -son or -dóttir (daughter) to it, and that is it. The next generation take their father's name and does the same. If for some reason father's name is not available, they will use a matronymic name instead. Many nations had this very same system at some point of time, but it seems Iceland is the only one that has kept it to these days. On the surface Icelandic names look pretty normal and very similar to other Nordic names, like, for example, Einar Benediktsson or Greta Salóme Stefánsdóttir. But in reality those names that seem to be surnames, Benediktsson and Stefánsdóttir are patronymic names derived from the corresponding fathers' names Benedikt and Stefán. And what it means is that the kins of the people with such 'surnames' will not get the 'surnames' of their parents, they will get new ones based on their patronymic names. Why? Because those are NOT surnames to beging with and there is NO surname in Iceland! Well, mostly no surnames just patronymic names.