Do you remember in The Player when studio honcho Griffin (Tim Robbins) takes the Icelandic girlfriend (Greta Scacchi) of the screenwriter he killed to a museum party? The Hollywood people don't know her, and someone goes "Whose daughter did he say she was?" Funny because true.
A friend from Iceland and his wife just had a baby (congratulations, Snorri & Lydia!), and he's posted an short explanation of the Icelandic naming system. It's patronymic (and sometimes matronymic), which means that a kid's surname isn't a family name, but a "son of whoever" and "daughter of whoever" indicator.
All of Scandinavia used to use a similar system, but they stopped at some point, which is why Minnesota is full of so many Gustafsons, and why Utah is freaking with Christensens. Iceland, meanwhile, is still mixing it up.
Icelandic last names [sturluson.com/snorrason]
Icelandic name system [wikipedia]
[update: while looking around for the official book of names for Iceland, I found NordicNames.de.]