The Chinese were first, introducing family names already about 2.850 B.C. The ancient Romans were then followed on the European continent; they usually had three names. For the German speaking regions, the history of family names starts in the 12th century. Here, for many centuries a single forename was sufficient to identify a person. However, even back then there were fashionable names so that the variety of names was reduced and led to a decline of Germanic forenames.
In addition, the population grew drastically between the 12th and 14th century. At some point there were, for example, three persons by the name of "Josef" in one village. Thus one name was not enough anymore to clearly identify a specific person.
The history of German family names - Part 1