Are there terms for referring to the different parts of a country's full title?

Take "People’s Republic of China" or "Kingdom of Norway", for example. I can refer to "China" or "Norway" part of the title as the country name (or geographical name). But if I want to talk about the political system, i.e., "People’s Republic of" or "Kingdom of" part of the titles, what is a word/phrase that I can use to refer to it?

If not, how can a new word for this be created using the ‘-nym’ suffix? What would be appropriate root word to use in this context?

(I know some countries don’t follow the above format, like UAE, but let’s ignore that for now)