I’ve been playing since 1967 and I have never seen a drummer kick a drum. I’ve seen them step on a pedal that in turn causes a mallet to hit a drum.
Perhaps a more accurate name would be a “pedal drum”.
Of course if we name drums based on the way they are struck wouldn’t we have ride stick drums and floor stick drums? Then what about snare drums? That name doesn’t describe how they are struck. Rather, the name describes an added component that changes the sound of what ostensively is a floor stick drum.
BTW, is it a drum set, a drum kit, a trap set, or something else?
This is starting to sound like Computer Science. That is, there are only two difficult things in CS - maintaining cache coherency and naming things.