My entire name is Icelandic. Initials: JGY. Yeah yeah, gettin' jiggy wid it, I heard it all.
My first name is my Icelandic grandmother's name, in good Icelandic tradition. (Even though it was my Thai mom that named me that!)
My middle name is my Icelandic father's first name followed by -dóttir. It's basically what my last name should have been, were I born in Iceland.
My last name is my Icelandic grandfather's first name followed by -son. It's what my father's last name was, since he WAS born in Iceland. I got his last name because I was born in America.
So I have two Icelandic last names, one for a son, one for a daughter. No wonder I've always been so confused.

Really, though, I like my name. It has basically four people's first names contained within it (if you include me), and they're all pretty much unpronounceable because Icelanders love their consonants. I've never minded having a difficult name, though it adds a few minutes to any official exchange when I have to spell it three times. In fact, I love my name.
There are no American names in my entire family (e.g. Stephanie, Jennifer, Kim, Amanda, etc... no offense to you folks), since they're all immigrants. And I plan to keep it that way, for originality's sake. I was ALWAYS the only one with my name, in any school or work scene... always original. I loved it.
And if someone is reading my name off a list (without having heard me say it first), I let them screw it up first, then correct them. Every. Single. Time.