姓 is a sound-and-meaning character. 女, “woman”, gives the meaning category, while 生 supplied the historical sound clue. The word once belonged to an older system of clan and lineage names whose distinctions changed over time; it would be too simple to read the component 女 as proof of one complete social system. This ancient-form sketch therefore shows the attested 女 and 生 structure rather than inventing a literal family scene.
A piece of culture
Family name comes first In Chinese names, the family name conventionally comes before the given name: the basketball player Yao Ming is 姚明, with 姚 as his surname and 明 as his given name. The word 姓名 follows the same order — surname, then name. Mandarin reads it xìngmíng; Cantonese reads it sing3 ming4. This order keeps family identity visible from the first character.