In today's Human-Robot Interaction (HRI) scenarios, a prevailing tendency exists to assume that the robot shall cooperate with the closest individual or that the scene involves merely a singular human actor. However, in realistic scenarios, such as shop floor operations, such an assumption may not hold and personalized target recognition by the robot in crowded environments is required. To fulfil this requirement, in this work, we propose a person re-identification module based on continual visual adaptation techniques that ensure the robot's seamless cooperation with the appropriate individual even subject to varying visual appearances or partial or complete occlusions. We test the framework singularly using recorded videos in a laboratory environment and an HRI scenario, i.e., a person-following task by a mobile robot. The targets are asked to change their appearance during tracking and to disappear from the camera field of view to test the challenging cases of occlusion and outfit variations. We compare our framework with one of the state-of-the-art Multi-Object Tracking (MOT) methods and the results show that the CARPE-ID can accurately track each selected target throughout the experiments in all the cases (except two limit cases). At the same time, the so -t-a MOT has a mean of 4 tracking errors for each video.