Now a Chinese name is simply written with the family name first and the given name next, and Chinese people commonly address each other with full names instead of given names. But historicaly, there are much more than that in names.
Surname. In ancient times two types of surnames, family names (xìng) and clan names (shì), existed.
Family name were surnames held by the immediate royal family.
Clan name, as fiefdoms in a feudal society were divided and subdivided among descendants, so additional sub-surnames known as shi were created to distinguish between different seniority of lineages among the nobles though they shared the same ancestor.
Register name (Pǔ míng) is a name recorded in a pedigree or genealogy.
Generation name, Bèifen, is one of the characters in a traditional Chinese name, and is so called because each member of a generation (i.e. siblings and cousins of the same generation) share that character, unlike surnames or given names.
Given names Míng are generally made up of one or two characters, and are written after the family name.
Milk name, Rǔmíng, are usually an alteration of the given name.
Nick name (chuòhào). There are two kinds of nicknames; one given by biological parents to a baby, and one given by the family or a child's friends to another child.
School name, Xuémíng, is the name that a child takes to go to school.
A Chinese style name, sometimes also known as a courtesy name (zì), is a given name.
Courtesy name is traditionally given to Chinese males at the age of 20, marking their coming of age, and usually based on the meaning of the given name.
Pseudonym, Hào, is an alternative courtesy name, was usually self-selected, without connection with given name or courtesy name. It may embody a person's character or use the name of one's residence.
Designation is an official name, description, or title, related to an an office or post.
Honorary title may be given after person's death.
Posthumous name (Shì hào) is an honorary name given to royalty, nobles, and sometimes others after the person's death. Posthumous names can be praises or deprecations.
Temple names (Miàohào) were given after death to an emperor or king.
Era name (niánhào) is the regnal year, reign period, or regnal title used when traditionally numbering years in an emperor's reign and naming certain Chinese rulers.
Alias, alternative name or fancy name.
Literary name or pen name is another title beside given name and courtesy name of a literati.
Buddhist monk has special buddha name, Fóhào, and Taoist has also Taoist name， Dào hào.
Below is the names of the First President of Republic of China, Sun Yat-sen.
Given name: Wén
Register name: Dé míng
Milk name: Dì xiàng
School name: Wén
Courtesy name: Zài zhī
Pseudonym: Rì xīn, Yì Xian, or Yat-sen in Cantonese language
Alias: Chungshan in Cantonese, or Zhōngshān in Mandarin, or Nakayama Shō in Japan.
Styled or Posthumous name: guófù, i.e. "Father of the Nation"