Providing intelligent support to surgical teams is a key frontier in automated surgical scene understanding, with the long-term goal of improving patient outcomes. Developing personalized intelligence for all staff members requires maintaining a consistent state of who is located where for long surgical procedures, which still poses numerous computational challenges. We propose TrackOR, a framework for tackling long-term multi-person tracking and re-identification in the operating room. TrackOR uses 3D geometric signatures to achieve state-of-the-art online tracking performance (+11% Association Accuracy over the strongest baseline), while also enabling an effective offline recovery process to create analysis-ready trajectories. Our work shows that by leveraging 3D geometric information, persistent identity tracking becomes attainable, enabling a critical shift towards the more granular, staff-centric analyses required for personalized intelligent systems in the operating room. This new capability opens up various applications, including our proposed temporal pathway imprints that translate raw tracking data into actionable insights for improving team efficiency and safety and ultimately providing personalized support.