It's called checkoff's gun because when you write a play you're supposed to make a list of all the props and check off the ones that you've used in the plot, to make sure you don't miss any.
It's called Chekov's Gun because every episode of the original Star Trek famously features Pavel Chekov firing his gun in the third act, due to Walter Koenig's contract stipulations.
it's called Cheque of Gun because they write you a check to go buy a gun. for shooting people etc.