How Chinese Names Are Built: Surname, Generation and Given Name
The first surprise for most people is the order. In a Chinese name the surname comes first, then the given name. So in the name 李清照, 李 is the family name and 清照 is the personal name. Written in English, it is often reversed to Qingzhao Li, which is where a lot of confusion starts.
Surnames are few, given names are many
China has a very large population drawing on a comparatively small set of family names. A handful of surnames account for a significant share of the population. The classic text known as the Hundred Family Surnames, compiled around the Song dynasty, lists several hundred, but far fewer are common in daily life.
The variety sits in the given name, not the surname.

How long is a given name
Most given names are one or two characters. Two is the modern default. A single-character given name is perfectly normal but is more likely to collide with someone else, which is part of why two-character names became more common.
A full Chinese name is therefore usually two or three characters in total: one surname plus one or two given characters. Occasionally a surname is two characters, which makes the full name four.
Generation names
In some families, everyone of the same generation shares one character in their given name. This is the generation name. If you meet two people who share a surname and one given character, they may well be cousins.
Larger clans historically kept a written sequence of characters, agreed in advance, so that each generation took the next one in order. The practice is less common now, particularly in cities, but it still shapes names in many families and remains a strong clue to family structure.
What a name is expected to do
A Chinese given name is chosen for meaning, sound and balance. Characters are picked for what they mean — light, clarity, kindness, a plant, a season. The sound matters too, since the same syllable can carry very different meanings depending on tone.
Unusual characters are a trade-off. They stand out, but they also cause problems on forms, in databases and for anyone reading the name aloud.
Writing it in English
There is no single correct convention. Surname first with no comma, as in Li Qingzhao, keeps the Chinese order. Surname last, reversed, reads more naturally in English contexts. What matters is consistency within a document, and clarity about which part is the family name.