I have written about the history of surnames in Europe here which will provide context.

The reason that patronymic surnames (i.e. last names derived from the first name of a person's father) are so prevalent is that the original purpose of surnames was for the convenience of lords/governments in keeping track of taxes, landholdings, and generational debts. So, for instance, calling someone "William Johnson" made it pretty evident that William was John's son, and he inherited all of John's land, debt, and/or tax burden when John died.

But patronymics were never the only type of last name, as explained in my post linked above. There were/are several different surname systems. Location of a person's home ("William Atwater", "William Hill"), a person's occupation ("William Smith", "William Carter"), or a person's physical description ("William White", "William Brown") were also often used in "byname" systems as well as in some patronymic systems, and such last names continue to be used in modern "fixed surname" systems where they don't change from generation to generation.