A follow-up to [this question][1]. In *A Song of Ice and Fire*, bastards "who have no name of their own" get a surname like Snow, Rivers, or Stone, based on where they are from.  Does this apply only to the illegitimate children of nobles, or to the illegitimate children of the small folk as well? 

Presumably, in a feudal society commoners do not have surnames at all, so it would be strange if their bastards did.

Just to clarify, I was thinking about cases when it is not known for a fact whether the child is a bastard of a noble.  For example, Mya Stone was not acknowledged by her father, yet she is still a Stone.  So then we have an interesting situation in Westeros: people who have last names are either nobles or bastards (with or without noble blood).

  [1]: https://scifi.stackexchange.com/questions/22178/how-do-people-know-john-snow-is-a-bastard-just-by-his-name