Back when there was a very limited stockpot of names, and there might be, for example, two Roberts in a village who had to be distinguished from one another, they began to be identified by nicknames and by the names of their fathers: one would be known as Robert Will’s son, the other Robert John’s son, and soon an elaborate system evolved based on the names of grandfathers and great-grandfathers.
Similar patronymic systems, with names meaning “son of”, took root in most cultures. In Danish, the suffix added was sen, in Swedish son, in French de, in Armenian ian, in Basque ez, in Norman fitz, in Scotland Mac or Mc, in Ireland O’, Mac or Mc, and in Wales, simply the letter s–Jones meaning John‘s son.
Though all these surname names relate to paternal lineage, in these days of last-name-first and boys-for-girls, there are a lot of patronymics that can work for girls as well: Mackenzie and Madison are good examples that have already been totally accepted. Some of the many other possible “son of” names follow–those that have been used for girls are starred.