Traditionally, Chinese could assume additional names at other times in their life. These include the zì 字 (called a courtesy or style name), acquired upon reaching maturity, and the hào 號 (called an art name), a self-selected nickname. These types of names have become rare since the latter half of the 20th century.
Chinese given names usually consist of two syllables (though it is also common to only use one). Those syllables can be any of the thousands of Chinese characters so the combinations are almost limitless. In practice some characters are chosen more often than others, such as Mei "beautiful" for girls. Sometimes the first character of the given name is shared by all members of a generation in a family (siblings, cousins, etc) - see generation name. Chinese parents do not typically name babies after relatives or famous people.