There are regions of Europe where last names were not passed from father to child. In some regions, particularly Scandanavia and parts of northern Germany, children were given a last name (a patronym) that was based upon their father's name. Some men who went in the Swedish miltary had "military" last names. And in some regions, the family's last name "went" with the farm on which they lived.
Usually in the United States, last names passed from father to child. But that's not always true when one crosses the pond.