Generative paradigm, especially powered by Large Language Models (LLMs), has emerged as a new solution to the next point-of-interest (POI) recommendation. Pioneering studies usually adopt a two-stage pipeline, starting with a tokenizer converting POIs into discrete identifiers that can be processed by LLMs, followed by POI behavior prediction tasks to instruction-tune LLM for next POI recommendation. Despite of remarkable progress, they still face two limitations: (1) existing tokenizers struggle to encode heterogeneous signals in the recommendation data, suffering from information loss issue, and (2) previous instruction-tuning tasks only focus on users' POI visit behavior while ignore other behavior types, resulting in insufficient understanding of mobility. To address these limitations, we propose KGTB (Knowledge Graph Tokenization for Behavior-aware generative next POI recommendation). Specifically, KGTB organizes the recommendation data in a knowledge graph (KG) format, of which the structure can seamlessly preserve the heterogeneous information. Then, a KG-based tokenizer is developed to quantize each node into an individual structural ID. This process is supervised by the KG's structure, thus reducing the loss of heterogeneous information. Using generated IDs, KGTB proposes multi-behavior learning that introduces multiple behavior-specific prediction tasks for LLM fine-tuning, e.g., POI, category, and region visit behaviors. Learning on these behavior tasks provides LLMs with comprehensive insights on the target POI visit behavior. Experiments on four real-world city datasets demonstrate the superior performance of KGTB.