Advanced wireless network localization technologies have driven numerous transformative applications. Despite their innovative potential, these technologies also raise critical privacy concerns. This paper introduces a privacy-by-design approach using beamspace technology. While initially developed for resource reduction, the beamspace technique is explored as a novel privacy-enhancing technology. The Cramér-Rao bound (CRB) is adopted as the performance metric, through which we can systematically quantify and control potential accuracy loss and privacy guarantees. The beamspace design problem is formulated to minimize the maximum CRB, while ensuring that the minimum CRB is above a specified threshold within the region where privacy guarantees are intended. We develop a beamspace design method to address the trade-offs in privacypreserving localization systems, which offers a systematic way to optimize accuracy while maintaining user privacy. Numerical results also show the impact of privacy restrictions on the performance of the wireless localization system.