This is a nice original “Rolex” stamped in movement frame and W&D in case (band not original). This vintage classic is a Collectors piece and does run.
These early wristwatches were sold to jewelers, who then put their own names on the dial. The earliest watches from Wilsdorf and Davis were usually hallmarked “W&D” inside the case back. In 1908 Wilsdorf registered the trademark “Rolex” and opened an office in La Chaux-de-Fonds, Switzerland.