What you are calling name changes are not surprising among Norwegian emigrants -- probably even emigrants from other countries.
My findings above were back to a Lars Olsen -- he had quite a number of sons and obviously at least some of them emigrated. Some might have chosen to use Olsen/Olson as an American surname and others may have used Larsen/Larson... it would have been just a choice.
I have one ancestral family where the entire family emigrated - some of the brothers used their father's Norwegian 'surname', some adapted their own Norwegian style patronymic and one actually chose to use the name of their original Norwegian family farm as an American surname. It didn't make any difference - they were still all siblings. I'm just thankful that none of them decided to call themselves Smith or Jones in America.
These messages will all wait until you can get to a location where you can carefully study and be able to give us feedback that will be useful.