A reader in Reykjavik writes:
A quick note - Icelanders don't use family names. They don't even have real family names - Sigurdardóttir means simply the daughter of Sigurdar; and Sigurdar really was the name of her father, so this does basically nothing to identify the specific person.
Any icelandic woman, whose father was called Sigurdar, is - by definition - 'Sigurdardóttir.' And they never use these except for most formal purposes and even then only in conjuncture with their first name. So strangely enough, the Iceland Reviews got it wrong; the title: "Sigurdardóttir ready to become Icelands PM" is just plain weird. She is simply Jóhanna and that's pretty much it.
I'm just psyched we have Dish readers in Iceland.