A friend researching his family history had mentioned that Jews in Europe started adopted last names as a family identifier as late as 200 years ago.
I wonder when and how were family names established in different cultures.
This page is a start (for family names of British origin).
http://www.familychronicle.com/surname.html
The Encyclopædia Britannica article on surnames says that the Chinese began using family names by imperial edict in 2852 B.C.E. while Turkey only established mandatory family names in 1935. In England, surnames began to be used around 1000 C.E., but took almost 600 years to become a universal practice.
Ancient Rome used family names, at least for the upper classes. They actually had two “family” names, as explained on this site.
The Scandinavian countries used to have a practice of assigning surnames, not by family, but by the father’s or mother’s first name or the farm on which one worked. This sight explains the process (if you can follow it).
Other European cultures developed just about as irregularly.
I believe that India had family names for quite a while, but whether they were used by everyone or only the nobility and military, I am not sure.
I am not at all familiar with naming in Africa or the Americas before the European expansion, but I suspect that they followed the same patterns of widely different usage among the many different groups.
As a bit of trivia - my father’s family didn’t have a surname until they came to the United States in 1900. It was assigned by Immigration, actually.