Regnal name

A regnal name, or reign name, is a formal name or label which refers to the years of the reign of a monarch or a pope. 
A monarch sometimes chooses a reign name which is different from his or her personal name.
A pope chooses a regnal name when he is elected. It becomes his new personal name.
The new name -- or sometimes the old one -- is followed by an ordinal number to create a unique name for the period in which the monarch is on the throne.