Norwegian Surnames (and How They Got That Way)
European Germanic and Latin surnames all have a similar history. In the earliest times in history, people had a given name, a patronymic and a surname. Scandinavian names kept an older European convention of a given name, a patronymic and a surname taken from the individual's farm or occupation. So, Amund Amundson would have been known as Amund Amundson Totland [name of his farm] in the old country. Because of this convention, surnames were not handed down from father to son, unless that son remained on the farm, or in that occupation. If a son moved, he would adopt a surname appropriate to his new circumstances, e.g. Amund Amundson Totland might become Amund Amundson Anglevik. In Iceland they still use this convention, and thus their phone books are listed alphabetically by first name. I should also add that a girl from this family would have typically been given the patronymic Amundsdatter (often abbreviated Amunds or Amundsdtr).
The above all reflects what was typical with naming conventions in France, Germany and England, as well, but several centuries earlier. Most of the following information is specific to Norway, but is generally true with some exceptions, for Sweden, Denmark and Iceland. The languages and cultures of the Scandinavian nations are so close that they can understand most simple grammar and vocabulary from each other's languages (my ancestors' bibles were in Danish, although they were all Norwegian).
For immigrants to this country, prior to about 1930 or so, some individuals chose to take the patronymic as an American surname, primarily when the farm name was hard to pronounce, hard to spell or perhaps because they had a less sentimental connection to the farm they lived on. Other immigrants shortened the farm name to sound more American (to their ears, anyway). One of my main ancestral lines is Sandbo. In Norway they spent a few generations on the Lillesandbu farm. My great-grandfather's name was Hans Knutssen Lillesandbu in Norway, which he formalized to Hans K. Sandbo upon his immigration. My own surname is a farm name, as well. Odegard is an Americanized version of the Norwegian Ødegård (which translates literally as deserted or desolate place). Farms were named after what people found when it was first formally settled as a farm. So an Ødegård was either a flat, featureless place, or sometimes a previously abandoned farm with buildings and no people.
Farms were often large enough to support several families who shared a surname, but not always a blood relation. Some families chose permanent surnames at different times, and were more likely to have done so earlier in Norwegian history the more urban their environment. Remote rural farms didn't adopt permanent surnames until the 1920s, but the process began in the early 1800s. Some families chose permanent surnames to honor an achievement.
Knowing the American surname of a Scandinavian ancestor is only the first of many steps toward learning more. It helps immensely to know what farm their family was from, or at least what part of the country they came from. Because farm names were typically descriptive (many might translate as Oak Hill, Riverside, Flatland, Mill Site, Pointy Rock and other such things), there are often several, and in some cases hundreds of farms with the same name across the country.
To add to the confusion, some farms split into smaller holdings, and were then identified by a modifying term. An individual from the farm Mosterhavn Vestre (the western holding on the farm Mosterhavn, near the town of Moster in Hordaland) may have adopted the surname Mosterhavn, or more likely Mosterhaven, or even Most. Some chose the name of the town because the farm name may have been too difficult for an American sensibility. Someone from the farm Spissøen Kræmmerleie very likely would have chosen the surname Moster, the town they lived near. Many of these are the immigrants who became Knutson and Olsen instead.
Another thing to know when looking at Scandinavian names and research is that Norwegian spelling was not formalized nationally until the 1920s or 1930s, and even then there are two formal spelling conventions accepted academically, New Norsk and Book Norsk. Some unique characters in Norwegian include: ø, å and æ. These are sometimes translated: o for ø, aa for å and ae for æ, but this is not consistently applied prior to the adoption of standardized spelling. As a result, our ancestors could have used any of these patronymic variations in official records: Amundson, Amunds, Amundsen, Amundsson, Amundssen, Amundsøn, Amundssøn, or Amundss (girls could be Amundsdatter, Amundsdotter, Amunds, or Amundsdtr and more). And, as referenced above, families moved around and sometimes changed their farm names, and other times did not, not to mention when individuals moved to an urban environment.
Knowing a bit about Norwegian geography can help, as well. The country is broken into Fylke, which are technically counties, but we can think of them as small states in Norway. I think there are seventeen Fylken. Each of these is separated into kommune or communities. There are usually several small towns in each kommune. Then, to confuse things just a little bit more, some records are cross-referenced not only to the political divisions just described, but also to the church parish, which often crosses kommune boundaries. This sounds confusing, because it is. My paternal ancestry comes from Øre parish, which used to be called Tingvoll parish, and Tingvoll is also a kommune which borders Gjemnes kommune where my ancestors were actually born. It took me a couple of years to figure out exactly what was going on with all that apparent nonsense, and I'm still learning.