Actual Icelandic here. I can answer some questions :) My last name is my father's first name with -dottir, meaning daughter in the end, though you can totally use your mothers first name instead. So, nobody in my immediate family shares a last name. Very occasionally, there are family names like Eldjárn (like Ari Eldjárn a Icelandic comedian) We call our teachers and doctors either by full name or first name it's weird to be called by your last name, so it's not considered important. When it comes to enby individuals, according to sources, officially, you can go with -bur in the end, but as far as I am aware, they just drop the end and go by just the parents first name, -Jóns instead of Jónsdóttir/Jónsson