The Norwegian naming patterns have changed through history. There are also regional differences. This text will try to explain the historical changes, and mostly with regard to the basic population.
It is convenient to look upon the first name as the real name. This was given to the child when it was christened. Way back in history only one 'first name' was the rule, but already before 1800 one can find many persons with two such names. Later on a child could be given three or even four 'first names', but only one of them was in use, perhaps two. Hyphenating two 'first names' is a newer custom.
The earlier use of 'last names' often confuses the genealogist of today, but was quite logical. Almost every person had a patronymic or father-name. If a man named Anders (first name) got a son called Jon, then the boy would be called Jon Anderssen, that is: Jon, the son of Anders. In some dialects the patronymic could be Andersson or Anderssøn, but the meaning is the same.
If Anders had a daughter called Anne, she would be called Anne Andersdatter, that is: Anne, the daughter of Anders. The spoken form, however, was more like Anne Anderste or Anderstet. Today Norwegian genealogists often use Andersdtr as an abbreviated form. The women used their patronymic all the life, married or not, but this custom began to change around 1900 or a little earlier.
Genealogists should use the patronymic as a clue for further search. If you find an ancestor named Ingeborg Nilsdtr, then you know for certain that her fathers first name was Nils. This helps to narrow the search. But of course it can be confusing to find a family where the fathers name is Anders Jonsen, the mothers name Ellen Hansdtr, and the children are named Jon Anderssen and Anne Andersdtr.
I should add that the patronymic could be dropped in the upper classes. In certain regions the patronymic was the only last name for most people, but as a rule one more 'last name' was added. They fall in two classes.
The most common pattern was adding the farm name, or 'address'. Let's use the example mentioned above. If Jon Anderssen settled on a farm called Bakken, he would be called Jon Anderssen Bakken, that is: Jon Anderssen, who lives at Bakken. If he moved to a farm called Vik, his full name would change to Jon Anderssen Vik.
Many families had a hereditary last name, often very old and in many cases of foreign origin. This was often the case in the cities or among high officials elsewhere in the country. If the family had a last name of this type, there was no need for a farm name. The hereditary names were seldom geographical names, as in the case of the farm names.
In the last decades of the 1800s a new pattern emerged, or rather two patterns. One was a radical change: A married woman could take her husbands patronymic. Anne Jonsen, that is: Anne, the son of Jon. Quite illogical! But the common people only copied the naming custom used by the richer people, they with the hereditary last names.
The other new pattern was this: The children got their fathers last name instead of a real patronymic. But in a 'transition period' that lasted until 1923, one can find old and new patterns side by side, even inside families.
In 1923 it was ordered by law that each family should have a hereditary last name and only ONE last name. Some families took a patronymic, others a farm name, and of course the old hereditary names lived on. But the result was great amounts of Olsen, Hansen, Nilsen and names like that - old patronymics. Later on many last names of this type has been replaced by constructed names to avoid confusion.
It's not necessary to say that the fathers last name also became the family name. The women lost their last name. Today the wheel has turned again. The women as a rule keep their last names after marriage. Yes, even the old custom with a real patronymic can be seen. Anne Andersdatter lives again!