How to determine the names of Western kings, such as Henry I and Henry II? Are there any rules?

There is no rule. Within a country, the first person named Henry is the first generation, and the second one is the second generation. They may be father and son, maybe grandfather and grandson, maybe more than ten generations apart.***Same point Even with the same name, they both became kings. In order, for example, Queen Elizabeth I of England died more than 300 years ago without giving birth to a child. The current queen is called Elizabeth II. She is not from the same family as I. of.