Most of the existing compositional generalization datasets are synthetically-generated, resulting in a lack of natural language variation. While there have been recent attempts to introduce non-synthetic datasets for compositional generalization, they suffer from either limited data scale or a lack of diversity in the forms of combinations. To better investigate compositional generalization with more linguistic phenomena and compositional diversity, we propose the DIsh NamE Recognition (DINER) task and create a large realistic Chinese dataset. Given a recipe instruction, models are required to recognize the dish name composed of diverse combinations of food, actions, and flavors. Our dataset consists of 3,811 dishes and 228,114 recipes, and involves plenty of linguistic phenomena such as anaphora, omission and ambiguity. We provide two strong baselines based on T5 (Raffel et al., 2020) and large language models (LLMs). This work contributes a challenging task, baseline methods to tackle the task, and insights into compositional generalization in the context of dish name recognition.