The "son/dotter" names in Sweden were patronymic. They were made from the father's given name + a possessive s + "son" for male children and "dotter" for female children. All Swedes could have a patronymic name (whether or not they used it).
Some Swedes used a surname in place of or in addition to their patronymic names. Adding a surname was not a name change. They still remained the son or daughter of their father. Town people were more likely to use a surname but of course many didn't and of course many rural people also used a surname.
Certain occupations used surnames. I think you need to read the articles about Swedish naming practices on this page so that you will understand those customs.
When did these people emigrate? There is a column listing a year of immigration in the U.S. Federal Census 1900-1910-1920-1930. When did they marry? There is a column in the U.S. Federal Censuses for 1900-1910 that tells the number of years a couple has been married and the 1930 census has a column asking how old a person was when first married.
Have you found these people in the STATE censuses for Iowa? (Those were taken in years usually ending with 5, as opposed to the federal censuses taken in years ending with 0. The 1925 Iowa State Census provides the names of the parents of every enumerated person. It is the best U.S. or state census I've ever seen.
Try to find a better birthdate for these people and try to find the mother's maiden name. Their death certificates should help with that.
If they married in the U.S., their marriage APPLICATION may have useful information, such as where they were born in Sweden (Were both born there?) and perhaps names of parents.
Many of us have found details about the Swedish origins of our ancestors and also the first years in the U.S. by checking out the fabulous records at the Swenson Swedish Immigration Research Center. The Swenson Center has a website but its extensive collection of records is NOT online. We need to go there to research or pay them to research for us.