Re-Identification systems (Re-ID) are crucial for public safety but face the challenge of having to adapt to environments that differ from their training distribution. Furthermore, rigorous privacy protocols in public places are being enforced as apprehensions regarding individual freedom rise, adding layers of complexity to the deployment of accurate Re-ID systems in new environments. For example, in the European Union, the principles of "Data Minimization" and "Purpose Limitation" restrict the retention and processing of images to what is strictly necessary. These regulations pose a challenge to the conventional Re-ID training schemes that rely on centralizing data on servers. In this work, we present a novel setting for privacy-preserving Distributed Unsupervised Domain Adaptation for person Re-ID (DUDA-Rid) to address the problem of domain shift without requiring any image transfer outside the camera devices. To address this setting, we introduce Fed-Protoid, a novel solution that adapts person Re-ID models directly within the edge devices. Our proposed solution employs prototypes derived from the source domain to align feature statistics within edge devices. Those source prototypes are distributed across the edge devices to minimize a distributed Maximum Mean Discrepancy (MMD) loss tailored for the DUDA-Rid setting. Our experiments provide compelling evidence that Fed-Protoid outperforms all evaluated methods in terms of both accuracy and communication efficiency, all while maintaining data privacy.