Short version: There were none!
The longer version follows below:
From the time before the Vikings and up to the year 1900, a Norwegian's 'name'
consisted of a given name or names only.
In addition, a name may have been added indicating whose son he was, but this was not a proper family name or surname.
If Hakon, Ole's father died and his mother remarried and the new husband's name was Hans, and if they had a son and called him Anders, his name would be Anders Hansen, but Anders' elder brother would still be Ole Hakonsen.
First husband and father: Hakon Svendsen
Mother: Kari Saxessdatter
First son: Ole Hakonsen
Second husband and father: Hans Nielsen
Second son: Anders Hansen
Daughters would be called - Hakonsdatter (daughter) and - Hansdatter
Since the probability was that there was more than one Ole Hakonsen around, the name of the farm they lived on as servants, tenant farmers or owners was normally appended to the given name(s), ensuring people knew from where Ole Hakonsen came or belonged. If he lived at a farm called Dulperud, he was probably known as Ole Hakonsen Dulperud, but in this case Dulperud is the address rather than a family or surname.
In the 19th century, due to the population increase and the difficulty to find jobs, people began to move. If Ole moved from Dulperud to a farm called Evenrud, 'the address' portion of his name, Dulperud, would change to Evenrud.
If later, Ole decides to move to America, he would arrive at a country where people were used to a family or surname, that is, one and the same last name for husband, wife and their children.
This would be a new custom for Ole. One last name for the whole family? Arriving at Ellis Island, Ole had to make a choice. Ole, would probably choose either his patronymic name of Hakonsen or his farm name of either Dulperud or Evenrud. In addition, he (or more likely, the immigration officer) might decide to change the spelling of the chosen name to make it easier for Americans to spell and pronounce.
In the end, Ole, son of Hakon raised on the Dulperud farm and with a job for two years as a farmhand at the Evenrud farm, could end up in the USA as Ole Evinrude.
Here in Norway, parish registers and census material will, however, still have him documented as Ole Hakonsen, possibly with the addition of the name of the farm on which he resided.
If you send us an email saying you are looking for Ole Evinrude born around 1880 we will probably not be able to help you.
If you say you are looking for Ole born about 1880 in Fet and that his father's name was Hakon, and that you know he had lived on farms called Dulperud and Evenrud, we might find him on our computers in a matter of seconds !
Except for a few rich families, mostly of Danish or German origin, who brought their family names with them to Norway before 1900, only in the early 20th century did people begin to use family or surnames in Norway; quite a few chose to use their farm names for this purpose.
As throughout time, so today, the custom of the family or surname is changing.
Many women now keep their maiden name after they marry. In such a case, if
Ole Hakonsen marries Ingrid Evenrud, their children may choose Hakonsen or
Evenrud, or both, as their surname(s). The complexity increases and, for
now, we can only speculate on what will happen when the next generation matures
and their children have to choose a surname.