Would they really have access or motivation to the flamboyant names of the elites? Or would they give them more mundane names, but still, in essence, a name that deals with common aspects of their lives, such as the highborn names do deal with descriptions of higher politics? Would the peasants be called "Sickle" or anything like that?
While we're waiting for someone to address lower class names in ancient Greece, you might be interested in this thread about heroic names. It includes information on general naming conventions (which would presumably include peasants), as well as a few asides on slave names. /u/Iphikrates gives a really nice answer here, but there were also others who contributed.