A car without a roof is called a convertible
Sun roof
the headliner or roof
Turret
In the auto industry, it is called the "head liner".
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
the light in the roof is called the interior or dome light. if the light is on a door it is called a courtesy light
The part is called a headliner, the material is usually cloth glue to a foam/composite board.