The integration of Large Language Models (LLMs) into personalized, patient-centric healthcare represents an emerging paradigm and transformative frontier in digital medicine. This new paradigm is reshaping how patients interact with digital systems, introducing new possibilities for patient-centred experiences. However, this growing field remains fragmented across technical, clinical, and interactional dimensions, making it difficult to synthesize common patterns and design principles. In this survey, we address this gap by presenting a comprehensive taxonomy that organizes current research across four human-centric pillars: Application Domains, Interaction Architectures, Data Integration for Patient Modelling, and Evaluation Methodologies. We emphasize how LLMs are being embedded into tools that support patient engagement, emotional support, and decision-making, raising essential questions about explainability, trust, safety, and the evolving role of clinicians in human-in-the-loop systems. Through this lens, our analysis reveals a critical tension at the heart of the field: while architectural innovation in areas such as Retrieval-Augmented Generation and multimodal systems is accelerating, progress is fundamentally hindered by persistent challenges in clinical reliability, data privacy, and justified skepticism from healthcare professionals. By bridging the perspectives of HCI, AI, and Health Informatics, we lay the groundwork for building more usable, equitable, and trustworthy systems for personalized care.