Sons and Dottirs

I'm very interested lately in Iceland, so today I had about 3 seconds of spare time to continue some reading about the 5th richest country in the world.

If I was born in Iceland, my last name would be Dennisdottir. If I had a brother, his last name would be Dennisson. What they do is take the fathers first name and add "son" if it's a last name for, well, a son, and "dottir" if it's for a dog. I mean dottir. Make that daughter. Björk's daddy was Guðmund.

Now, what was my daddy's name?