What's behind a name?
My first name has the English corollary "Christian". In Icelandic, the two n's indicate male -- the female version of the name being spelled "Kristín". By Icelandic patronymic tradition, as inherited from the Norse vikings who first set foot on the island in 874 AD, there are no real "last names" in Iceland: A person is either the "son" or "daughter" of his/her father. Thus, if your father's first name is Donald, and you are male, you would be Donaldsson (first 's' is the posessive, then add 'son'), or Donaldsdóttir, if you are female.
Hence, females don't change their "last name" when they get married; it would seem strange that they would become someone elses daughter, or, even worse, suddenly be the "son" of their husband's father. Which is why my wife's name is still Katrín Elvarsdóttir.