In multi-turn dialogues, large language models face a critical challenge of ensuring coherence while adapting to user-specific information.. This study introduces the persona knowledge gap, the discrepancy between a model’s internal understanding and the knowledge required for coherent, personalized conversations. While prior research has recognized these gaps, computational methods for their identification and resolution remain underexplored. We propose Conversation Preference Elicitation and Recommendation (CPER), a novel framework that dynamically detects and resolves persona knowledge gaps using intrinsic uncertainty quantification and feedback-driven refinement. CPER consists of three key modules: a Contextual Understanding Module for preference extraction, a Dynamic Feedback Module for measuring uncertainty and refining persona alignment, and a Persona-Driven Response Generation module for adapting responses based on accumulated user context. We evaluate CPER on two real-world datasets: CCPE-M for preferential movie recommendations and ESConv for mental health support. Using A/B testing, human evaluators preferred CPER’s responses 42% more often than baseline models in CCPE-M and 27% more often in ESConv. A qualitative human evaluation confirms that CPER’s responses are preferred for maintaining contextual relevance and coherence, particularly in longer (12+ turn) conversations.