So as I find more and more DNA matches with Norwegian-American relatives who tell me “Oh we have an Andressen or a Larsen too,” how do I explain what little use that is? I try saying, “Well in Norway before the late 1800s most people used their father’s name (so Jonsen means the son of Jon) and perhaps their farm name for a surname. So please tell me what locality your family was from and the farm name if you know it.” Plus Per might be Peder in a different document and other names have other variations. Still one can’t complain, there are an enormous number of Norwegian records online and the records go back to at least the 1500s in most localities.
I have found two resources which explain the naming practices quite well:
John Føllesdal also has an excellent website hosted by ancestry.com explaining how to research your ancestors in Norway.