Is there a formal term for functions that have static state across executions?
Not that I know of, but "stateful function" is reasonably descriptive.  In informal conversation, that's what I'd use, as long as I suspect the audience will understand what I mean.  In formal writing, I might still use the same phrase but also provide a careful definition of what I meant by that phrase.  Really, that's a large part of what "formal" writing is about: it's about being precise about what you mean.