In the auto industry, it is called the "head liner".
The part is called a headliner, the material is usually cloth glue to a foam/composite board.
The roof
A car without a roof is called a convertible
Sun roof
A convertible is a car that has a detachable roof. They come in two varieties, hardtop and soft top(rag top). Hardtop means they have a rigid roof that can be put on, soft top means they have a foldable cloth roof that can be erected.
the headliner or roof
Turret
convertible Drop head Roadster (if it is a 2 seater)
Some cars have those removable tops on them or the tops of the cars go back so it has no roof, which are called convertibles . As the car can change from closed top (roof) to an open top (roof).
A car that has no roof is merely roofless, but the name for such a car that has a retractable or removable roof is a convertible.
no <><><> The first car did not have a roof at all.
roof scoop or sun roof