I’m talking about when a family names a son after their father, and that son names a son after himself, and so on.
For example, the King Louis’ (although they weren’t always a son, but they were directly related (I think)).
Edit:
To clarify,
I’m looking for a name that spans several generations in the same family line, like a lot of kings did.
For example, there were (if I remember correctly) around 10 King Louis(es? ‘? I’m unsure what the plural of Louis is).