Is there a separate name for back seat in a car?

Well, back seats or rear seats is about it. In sports cars, that are classed as 2 + 2, meaning the rear seats are only small or fit for children, they are sometimes called occasional seats. Some old cars, used to have a seat which appeared when the boot lid was opened. These were accessed by striding over the rear seats, or standing on the back wheel. In England, this type was called a "Dickie" seat, and in America a "Rumble" seat.

The removeable part that you sit on, is sometimes referred to as a 'Squab'.