What is the term for adjectives attached after names? For example, there is terrible in Ivan the Terrible. Are these counted as post-positive adjectives?
This particular usage itself - an adjective following and considered part of a name - is most commonly referred to in English as an epithet.
Grammatically, it is treated simply as a part of the person's name and so as a proper noun. In English we do not put a comma between the adjective and the name, as it is considered to be a unit. It is formed, as Jlawler says, by a noun and an adjective in apposition.
EDIT: Some seem to think that agnomen applies here due to a definition found in "Webster's" and Wikipedia. But an agnomen had a rather specific use as part of a Roman person's name. The articles point out that nowadays we have parallel constructions that are similar to agnomina. Examples they give are "Stonewall" Jackson and "Iron" Mike Tyson and even, yes, Aristides the Just. You will notice that Stonewall and Iron are nicknames and do not come after the name. So agnomen is a more generic term. But Ivan the Terrible, Alexender the Great in particular are epithets.
They're just appositives, though of course the Greeks had a word for them, as Shyam points out.
The adjectival constructions are just normal generic uses of adjectives as appositives:
- Peter the Great (One), Ivan the Terrible (One), etc.
You can also use nouns with the same appositive construction:
- Peter the Hermit, William the Bastard, my son the doctor, etc.