>>> The prototypical Chinese name has three characters, a single surname followed by a two-character given name. A smaller number of Chinese people only have a single given name, and a very few have two surname characters.

>I'm not sure if this is correct.

It's not. The distribution of one- and two-character given names is pretty even in China.

>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).

You know, maybe we should change how we think about the ordering. Instead of family-given or given-family, it's clearly restricted-arbitrary.

From the friendly article: "As in other languages, there are always exceptions."

Wikipedia goes into extreme detail: https://en.wikipedia.org/wiki/Chinese_name

I would not characterize the number of people who have single given names as "small". This also differs a lot by region.

it is missing one option. in some areas the middle character is a generation name. that is, that character is the same for all members of that generation.

so the thee characters would be: family-generation-given name