You may feel special and believe that you are getting personalized care when your doctor remembers your name and your unique medical history. But, what if it is an AI doctor and not human? Since AI systems are driven by personalization algorithms, it is possible to design AI doctors that can individuate patients with great precision. Is this appreciated or perceived as eerie and intrusive, thereby negatively affecting doctor-patient interaction? We decided to find out by designing a healthcare chatbot that identified itself as AI, Human, or Human assisted by AI. In a user study assessing Covid-19 risk, participants interacted twice, 10 days apart, with a bot that either individuated them or not. Data show that individuation by an AI doctor lowers patient compliance. Surprisingly, a majority of participants in the human doctor condition thought that they chatted with an AI doctor. Findings provide implications for design of healthcare chat applications.