So up until the Dominion War, seems likely promotion was fairly slow. And Chekhov was quite junior, with a couple of great big black marks on his record (like stealing the Enterprise).
Yet if Star Trek: Renegades ever reaches the stage where we consider it canon, Chekhov did indeed become a Captain. And is currently an Admiral!
The USS Chekhov btw I suspect is named for the playwright.
for the Trek character, Chekhov
for the playwrite, so if the spelling should be the tipoff.