Given that the entire population of Iceland is not much more than Brighton, there's a fair chance that most of them are related to each other.
Having said that, they don't really have surnames, if I remember correctly. Rather their second names reflect the immediate father (or mother) of the child and not the historic family lineage.So this bloke's second name ( Gudmundsson)simply means that his father's first name was Gudmund, and Bjork's second name (Gudmundsdottir) simply means that her father's first name was also Gudmund. Gudmund is quite a common first name so it's unlikely to be the same Gudmund (if it was, they'd be brother and sister), and they're not that likely to be closely related.
