This study addresses the challenge of ambiguity in knowledge graph question answering (KGQA). While recent KGQA systems have made significant progress, particularly with the integration of large language models (LLMs), they typically assume user queries are unambiguous, which is an assumption that rarely holds in real-world applications. To address these limitations, we propose a novel framework that dynamically handles both entity ambiguity (e.g., distinguishing between entities with similar names) and intent ambiguity (e.g., clarifying different interpretations of user queries) through interactive clarification. Our approach employs a Bayesian inference mechanism to quantify query ambiguity and guide LLMs in determining when and how to request clarification from users within a multi-turn dialogue framework. We further develop a two-agent interaction framework where an LLM-based user simulator enables iterative refinement of logical forms through simulated user feedback. Experimental results on the WebQSP and CWQ dataset demonstrate that our method significantly improves performance by effectively resolving semantic ambiguities. Additionally, we contribute a refined dataset of disambiguated queries, derived from interaction histories, to facilitate future research in this direction.