My understanding is that most Norwegians in the 1800s had two surnames: 1) the patronymic surname (father's first name plus -sen for a son or -datter for a daughter) and 2) either a farm name (gardnavn) if they were from the country or an "etternavn" (other name) if they were from the city. My immigrant great grandfather's full name was Hans Olsen Bugge. He was a fisherman from a city -- his father's first name was Ole and Bugge was their etternavn. The etternavn stayed the same from generation to generation but the patronymic usually changed with each generation.
Norwegians who immigrated to America could only have one surname here and they had to pick one. Some went for the patronymic and some went for the farm name or the etternavn. My great grandfather took the patronymic Olsen and forgot Bugge, but his brothers dropped Olsen and used the etternavn Bugge instead. My great grandfather's certificate from sailing school in Drammen, Norway, in 1870s clearly recorded his full name as Hans Olsen Bugge, though.
See the general discussion about Norwegian names on the University of Bergen website:http://digitalarkivet.uib.no/sab/howto.html#Names
Excerpt: "On the whole, the immigrants were not very particular about which surnames they adopted. The most important factor was apparently whether the name could be written and pronounced in English. In America, names such as Nelson and Johnson were already widely known and much easier to pronounce than most Norwegian farm names. Even if the original farm name was retained as a surname, it was often altered and modified so much under the influence of the new language that it is now unrecognizable."