If city lists are extensive enough, an overlap is no problem at all. The game just needs to check when founding if a city with this name already exists on the map. The PRC can include all of Zhou and Ming cities that still exist today, but hopefully it is not the other way round as well and Zhou only found cities of their time.
It's not even a problem when razed/renamed cities are not taken into account, as there is historical precedence for that (e.g. Bern was founded and named when Verona, whose German name was Bern, left the Empire).
I for one also don't have a problem with the same city being on the map under different names - as long as they are different enough, like for the Ottomans and Byzantines or Egypt and Arabia.
There are situations when it is really hard to avoid, such as with Rome (would you prefer to exclude it from Roman or Italian civ?), Moscow (do you take it away from 17th century Russia or Soviet?), or numerous very different Islamic civilizations which all used Arabic language and covered similar areas, with the exact same main cities.
You simply can't take, for example, two Islamic civilizations from Egypt and don't give freakin Cairo to one of them and instead some random obscure town.
Or what if you'd like to have several incarnations of France, Germany and England? Who gets Paris and London and who gets some obscure town instead, from "extensive city lists"?
We get several Chinese civilizations in the game, but cities such as Beijing and Nankin were absolutely crucial to many Chinese civilizations for many centuries, under the same names.
That's not that easy question, you can't always handwave it with "extensive city lists", that's why I am asking about tu - its interesting
And remember, the situation is differented from civ. In civ there are a lot of civs (much more than actual number of player slots in a game) which are mostly singular and general in nature, so there is a small chance there will be any two conflicting name lists in one game. In Humankind you are (unless AI players are destroyed completely) very likely to get China 1, then second player with China 2, and then third player with China 3, as there are very few civs choosable per era and some cultures appear under many ages.
There is, IIRC, confirmed Ming and Peoples Republic of China in this game. Both have Beijing as their capital in real life. It is likely they will be taken by two different players in the same game. Which one is getting Beijing on their name list? Which one gets Nanjing? Its like deciding whether to take away London and York from England lol. Maybe those names are simply duplicated and nobody cares, as with Tripoli in Lebanon and Tripoli in Libya, or many Alexandrias?
Now I have realized that I have no idea how cities in this game are named in general with its "changing cultures" concept - do your cities change names with eras and other cultures, or you have an option to change them, or does your culture name newly settled cities in this era but does not rename previous cities... Etc.