What was the room at the top of a castle tower called?

I believe it is called a turret.

Turret: A small tower; more specifically the buttressed corner of a keep that provided extra protection to a most vulnerable part of the building. (A corner, if 'blind' to the field, could be undermined and bring down parts of two walls.)

Room at the top of a castle tower is sometimes called the Donjon (Latin: Dominant Point) or Dungeon either inside the Keep or the Keep itself, the strongest part of the castle. Once the Lord's quarters, later the prisons where notorious prisons were kept before dungeons were built underground.

It can also be used as a strong room for storing treasure e.g Tower of London although they are currently stored in the Waterloo Barracks not in the Donjon.