A finishing/covering element for a component in a vehicle passenger compartment has a front surface facing, in use, the inside of the passenger compartment and a rear surface facing, in use, the component on which the finishing/covering element is fitted; the finishing/covering element is manufactured by moulding a thermoplastic material in a mould, which has a first and a second forming surface facing one another; the first forming surface forms the outline of the front surface and is embossed so as to form a corresponding embossing on the front surface, without further treatments and/or coating operations and/or processing on the front surface after the moulding; at the same time, the moulded thermoplastic material comprises a thermoplastic polyurethane reinforced by reinforcement fibres.