Some of the early Norman nobility arriving in England during the Norman Conquest differentiated themselves by affixing 'de' (of) in front of the name of their village in France.
The practice of using family names spread through the Eastern Roman Empire and gradually into Western Europe although it was not until the modern era that family names came to be explicitly inherited in the way that they are today.
The use of family names is widespread in cultures around the world.
Each culture has its own rules as to how these names are applied and used.
In none of these cases, though, were these names considered formal parts of the person's name, nor were they explicitly inherited in the manner which is common in many cultures today.
In the Roman Empire, the bestowal and use of clan and family names waxed and waned with changes in the various subcultures of the realm.