Most refer to it as shooting from "Close Contact" which is the point in the weapon presentation where the gun has cleared the holster and has been rotated toward the target but before the shooter begins to push the weapon out toward the target and acquire the sights.
More like shooting from the rib cage than the hip.
I teach firing from retention, done when the antagonist is literally on top of you. And how to index the gun to the target at extreme close range.
When you say firing from the hip all I see is the old cowboy movies.