Chinese Names
Chinese naming is pretty straightforward: family name, then one or two characters chosen nearly at random. That's the short version.
Long version:
There are a lot of family names (several hundred according to The Other Wiki), but a handful dominate: Zhang, Li, Wang, a couple dozen others. These are usually one syllable, though two syllable surnames do exist. Perhaps the most famous one is Zhuge, as in Zhuge Liang (and Sima, as in his rival Sima Yi) from the Romance of the Three Kingdoms.
These surnames tend to be clustered by region, with certain names being particularly common in a particular province. Many Taiwanese are named Chen, for example.
Generally speaking, any character(s) can be used for a given name, though families avoid repeating names or naming children after famous people. In most of the Imperial history, it was criminal to use the names, or the homophones of the names, of the current Emperor and all previous emperors of the same dynasty. In practice, names with bad sounds or unpropitious strokes and overly complicated or obscure characters are also avoided. Furthermore, while the given names can be just one or two random characters strung together, most parents tend to work in some auspicious meaning/symbolism. Those born during the Cultural Revolution, for example, tend to have given names with the character for "red", "people", "revolution", "army", "steel" and such revolutionary socialist concepts worked in somehow.
In some families, all the children of a generation will share one character in their name. Even if a particular generation did not actually do so, they may still be referred to as the '__ Generation' for genealogical purposes or for determining precedence and protocol at reunions.
Nicknames are common, though the lack of common names means that there are no 'standard' nicknames like Tom for Thomas. Children are frequently called by one syllable repeated twice and people may receive other nicknames later in life.
Many Chinese figures are not generally referred to by name. Confucius and Sun Tzu are not names per se, but rather titles that are conventionally translated 'Master Kong' and 'Master Sun.' Similarly, Lao Tzu is the Old Master.
Almost all famous historical figures you come across will have at least two or three names. Taking up "style names" were popular for public use while reserving their real names for intimates. The Romance of the Three Kingdoms provides a number of examples: Zhuge Liang is Kongming, Zhao Yun is Zilong, and so on. Each of them would have the given name, and then have a "zi", which is basically another given name for more intimate occasions, and probably at least one "style name" (as mentioned above). This results in I Have Many Names.
More recently, Sun Yat-Sen is generally known in Chinese as Sun Zhongshan instead of his 'official' name used in family records. Yat-Sen itself a romanization of the Cantonese pronunciation of the name his teacher took when he first went to school, while "Zhongshan" was a pseudonym adopted while in exile in Japan, where he took the surname Nakayama (read Zhongsan in Chinese) from a sign on a palace near Hibiya Park in Tokyo. (His legal name is Sun Wen). On the other hand, Chiang Kai-shek is another name that passed into English via Cantonese—but that's not his legal name either; his legal name is Zhongzheng, adopted relatively late in his life; Kai-shek (Jieshi in Mandarin) is his style name.
Amusingly, China's enormous and growing population has led to a number of problems, including one less well-known than most of the rest: not enough names. Chinese naming traditions mean that there are a fairly restricted number of possible names, and therefore a lot of people with the same name (rather like all the Joneses in Wales). As a result, younger Chinese people have developed a habit of giving themselves a nickname, often picked entirely at random, to distinguish from each other. There are a large number of Chinese kids called things like Wang Harry Xiao or Ling Michael (as in Jordan) Hue.