Looking for name of common numbered lists

I'm looking for any recognized name or perhaps to coin a term that that refers to a proper name given for a list of things that is regularly defined by the number of things in a list:

• Seven Deadly Sins
• Four Horsemen of the Apocalypse
• Seven Wonders of the Ancient World
• Five Stages of Denial

Has anyone heard of a name for what these are called?

If you had to come up with a name, what would it be? Enumeronym? (Hate pairing Latin and Greek roots, but...)

"Enumeration" or "enumerated set" generally describes such a list. I'm not aware of any more precise word for it. As for creating a word for it, as you asked, I'd say you're on the right track using "enumerate" as the root word. "Enumerism" perhaps, which follows a similar construction as euphemism, criticism, etc.