

Seeing as people can change their own name to whatever they want, including if there is no preceding generation with that name, then no, there’s no particular issue with suffixes on names.
I’d like to point out that in the English-speaking world, the English (and now British) Monarchy increments the generation number without regard for the immediately preceding generation. As in, Elizabeth II was crowned 300+ years after Elizabeth I. So it is well accepted that ordering doesn’t necessarily matter and there is no hard rule against it.





I can concede this.
Whereas this cannot possibly make sense, because knowing which person is which would still be relevant after they’re all dead. See Pliny The Elder versus Pliny The Younger, Alexander Dumas (father vs son), and MLK (senior and junior).