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regnal number

n. An ordinal number that distinguishes a monarch from others of the same name

Wikipedia
Regnal number

Regnal numbers are ordinal numbers used to distinguish among persons with the same name who held the same office. Most importantly, they are used to distinguish monarchs. An ordinal is the number placed after a monarch's regnal name to differentiate between a number of kings, queens or princes reigning the same territory with the same regnal name.

It is common to start counting either since the beginning of the monarchy, or since the beginning of a particular line of state succession. For example, Boris III of Bulgaria and his son Simeon II were given their regnal numbers because the medieval rulers of the First and Second Bulgarian Empire were counted as well even if the present Bulgarian state dated only back to 1878 and were only distantly related to the previous Bulgarian states. On the other hand, the kings of England were counted starting with the Norman conquest of England. That is why the son of Henry III of England is counted as Edward I even though there were three Edwards before the Conquest.

Sometimes legendary or fictional persons are included. For example, the Swedish kings Eric XIV (reigned 1560–68) and Charles IX (1604–11) took ordinals based on a fanciful 1544 history by Johannes Magnus, which invented six kings of each name before those accepted by later historians.

In any case, it is usual to count only the monarchs or heads of the family, and to number them sequentially up to the end of the dynasty. A notable exception to this rule is the German House of Reuss. This family has the particularity that every male member during the last centuries was named Heinrich, and all of them, not only the head of the family, were numbered. While the members of the elder branch were numbered in order of birth until the extinction of the branch in 1927, the members of the younger line were (and still are) numbered in sequences that began and ended roughly as centuries began and ended. This explains why the current head of the Reuss family is called Heinrich IV, his son Heinrich XIV and his son Heinrich XXIX.