In recent history, a lot of people did not have surnames of family names. They used the name of their father (rarely their mother) as to distinguish who they were. (see: http://en.wikipedia.org/wiki/Patronymic )
An example from the Netherlands:
Jan has a son named Pieter, who will then be named Pieter Janszoon (or Jansz. in short form). Sometimes people have both a surname and a patronym: Michiel Adriaansz. de Ruyter.
In some countries this is still the way people are named.
Because sometimes patronyms and surnames are used simultaneously, this should be a seperate field.