They sure can.
Chinese emperors are known by an unique name they select for their reign. For example, [Kangxi](https://en.wikipedia.org/wiki/Kangxi_Emperor) was actually born Aisin-Gioro Xuanye. In fact, year numbers are reset whenever a new emperor takes the reign, a practice that [continues today in Japan](https://en.wikipedia.org/wiki/Japanese_era_name), so it’s practically important to not repeat the name of the reign.
In parallel, there’s a general [naming taboo](https://en.wikipedia.org/wiki/Naming_taboo) against speaking or writing the given names of exalted persons, so “Charles III” would not only not be honoring the previous Charleses, it would be considered grave disrespect.
So there’s no “why”, it’s just the culture.
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