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
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).
convertible Drop head Roadster (if it is a 2 seater)
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