“A girl gets her last name after one of her parents first name. Then dóttir, meaning daughter, is added to notify that it is that person’s child. It is the same with boys but instead of dóttir, they have a son added at the end of the name.”
Likely of Norwegian tradition ie. Olufson, Nelson, Anderson etc.
It’d be a bit of a challenge building a family tree. No common last names through generations, and many unrelated people with the same last name.
And I realize the English had similar traditions with last names like John-son and Jack-son, etc. But I guess that was abandoned centuries ago.