I'm not sure if this is correct. IIRC, in at least some areas/families, it's a tradition to alternate between giving a one or two character name from generation to generation. So if your parent has a two character given name, you'll have a one character name, and vice-versa.
Another interesting characteristic of Chinese names is that given names are very diverse and varied, while family names come from a small set (something like a hundred or so). This is opposite from the West (or at least America) where given names are pretty restricted (e.g. lots of Johns and Emilys) but family names have a lot of variation (probably due to all the immigration).