A damper housing disposed on a center axis includes an extended mains section and a narrowed end section. The narrowed end section has a second predetermined wall thickness less than the first predetermined wall thickness of the extended main section. An intermediate conical section, connecting the narrowed end section and the extended main section, has an intermediate conical section wall thickness equal to the second predetermined wall thickness at an internal inclination angle relative to the center axis. A method for manufacturing the damper housing using a preformed tube, a first broaching die, a calibrating mandrel, and a swaging die is performed by compressing the preformed tube between the first broaching die and the narrowed head of the calibrating mandrel and compressing the preformed tube between the swaging die and the intermediary section of the calibrating mandrel to form the narrowed end section and the intermediate conical section, respectively.