Upvote:4
Yes, both. In traditional Norse culture, it's "son of", e.g. Leif Erikson was the son of Erik the Red (discoverer of Greenland). Most western cultures at some point converted such names to a family name, thus you would have generations of Eriksons. But Iceland keeps the traditional Norse system (at least partly). Women take the '-dottir" (daughter) suffix, instead of "-son" (or sometimes "-sen"), sometimes with the mother's name rather than the father's.
(Note that Russian names also work somewhat similarly, with a patronymic middle name, e.g. Nikita Sergeyevich Khrushchev was the son of Sergei Khrushchev.)