Discovering customer intentions in dialogue conversations is crucial for automated service agents. However, existing intent clustering methods often fail to align with human perceptions due to a heavy reliance on embedding distance metrics and a tendency to overlook underlying semantic structures. This paper proposes an LLM-in-the-loop (LLM-ITL) intent clustering framework, integrating the semantic understanding capabilities of LLMs into conventional clustering algorithms. Specifically, this paper (1) investigates the effectiveness of fine-tuned LLMs in semantic coherence evaluation and intent cluster naming, achieving over 95\% accuracy aligned with human judgments; (2) designs an LLM-ITL framework that facilitates the iterative discovery of coherent intent clusters and the optimal number of clusters; and (3) proposes context-aware techniques tailored for customer service dialogue. As existing English benchmarks offer limited semantic diversity and intent groups, we introduce a comprehensive Chinese dialogue intent dataset, comprising over 100k real customer service calls and 1,507 human-annotated intent clusters. The proposed approaches significantly outperform LLM-guided baselines, achieving notable enhancements in clustering quality and lower computational cost. Combined with several best practices, our findings highlight the potential of LLM-in-the-loop techniques for scalable and human-aligned intent clustering.