The name can be either Anglo or Scandinavian. The Scandinavian spelling "Albertsen" means the same in English, "son of Albert". Like many other surnames, either by choice or force it became Anglicized to Albertson. I know many "Albertsons" in Southern New Jersey are descendent from the original Swedes who settled the area in the early 1600's. The surname Albertsen gradually changed to Albertson once New Jersey was controlled by the English after the 1660's