what is the rear window overhanging ‘shade/shelf’ thing on suv’s called and what is it for?
Are you referring to the structure that contains the center-mounted brake light?
If so, it is a “spoiler” that is there to manage airflow over the rear of the vehicle.
It can also help–to a very small extent–to keep the rear window clean.
If you are talking about the movable cargo cover – it’s to cover anything in the back of the car that you don’t want exposed.
There is no rear window shade.