Under that cover is access to override the shift interlock system. You know, key on then foot on the brake to shift? You can stick a pen or thin screwdriver in the hole to depress a release button so the shifter can be moved to neutral without key or brake pedal needed. Mostly used for towing when a battery is dead so vehicle can go into neutral.
I would call it shift interlock override cover but I don't know the technical term.