They were given by convenience and circumstance, not by birth. Surnames were last names that a family took, and passed on to their offspring, generation after generation. Many surnames originated as bynames that the family kept. Surnames started in the 1300's in Western Europe and were in general use throughout most of Europe by about 1500. Relationship names are last names that denote being connected to a family.
Occupational names are last names derived from an occupation.
Epithets are not really true names but phrases or terms which describe a characteristic of the person. Epithets can represent a physical characteristic, a character trait or even an event in a person's life. Last names that are relationship, occupational or locative in nature are fairly easy to locate. But for the most part, these last names are easy to find. Epithets seem to be a very easy concept.