The paper concerns the morpho-syntax of Chinese personal names, including given names, family names, and full names. The two varieties of Chinese discussed are Mandarin and Xining Chinese. Given names are subject to a condition ruling out monosyllabic given names occurring as free words. Family names are not subject to such a condition. A corpus study and a judgment experiment have been conducted to verify this difference between given names and family names. The condition is satisfied by either combining two or more monosyllabic given names to form compound given names, or by combining a given name with a family name, or by reduplication. Given names and family names, like other content words, are composed of a root and a categorizer. The reduplication that applies to given names in Chinese is the same operation that applies to monosyllabic nouns in Xining Chinese: reduplication occurs, with no semantic effect, when the categorizer copies the phonological matrix of the root. Family names in Chinese need not, and cannot undergo reduplication, being combinations of a root and a distinct family name categorizer that does not allow reduplication. While compounds made up of two or more given names are symmetric and non-compositional, made up of two coordinated names, full names made up of a family name and a given name (single or compound) are asymmetric endocentric compounds in which the given name is the head and the family name is an attributive modifier. A full name is thereby formally a given name. Pet names and so called generation names are discussed as well.