Chinese names are in this order: surname personal-name.
The personal name part could be just one character, e.g., Ling (in Huang Ling), or it could be two characters, with one of them being the generation name.
The two-character personal name version is the one that has room to contain the generation name. For example,
Li Guo Qiang
Li Guo Jun
Li Guo Fu
Li Guo Ming
It's easy to see the common denominator "Guo" in the series above. They are the "Guo" generation.
The generation name can also be in the second character position, i.e.,
Li Qiang Guo
Li Jun Guo
Li Fu Guo
Li Ming Guo
At one glance, one would immediately know that they're the same generation, but not if they're brothers or cousins.
Generation names are traditionally / historically more for boys, as they're the ones passing on the clan name.
If girls are given a generation name, it'd usually be a different one for their series, partly because girls' names tend to be more feminine (flowery, fragrant, gentle, elegant), while boys' names would be masculine (loyal, strong, brave).
An example of the practice for girls' names, using the common denominator marking their generation:
Li Mei Ling
Li Mei Luan
Li Mei Feng
Li Mei Xiang
The generation name Mei can also be the second character of their personal name, but it has to be consistent for the whole range, i.e.,
Li Ling Mei
Li Luan Mei
Li Feng Mei
Li Xiang Mei
The one-character personal name version is particularly common in post-1949 China, although there are historical figures, going as far back as B.C. days, with single-character personal names, e.g. (just to name a few that come immediately to mind),
蘇秦 / 苏秦 / Sū Qín
382–284 B.C.
political consultant and philosopher of the Warring States Period
蘇武 / 苏武 / Sū Wǔ
140–60 B.C.
diplomat and politician of the Western Han dynasty
岳飛 / 岳飞 / Yuè Fēi
1103–1142
a military general of the Song dynasty
The generation name practice, therefore, cannot apply to this category.
(from googling)
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Traditional Chinese generation names (字, zì) were historically much more common and strictly used for boys as part of patrilineal lineage, marking their place in the clan, while girls often had a different generation name or none recorded in family books, though some families gave sisters matching generation names. While this practice has significantly declined in modern China due to urbanization and changing customs, the tradition was strongly male-focused, marking generational hierarchy, with females often having separate naming conventions.
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