With the arrival of large language models, generative retrieval (GR) has emerged as a new paradigm, which generates identifiers of documents relevant to a given query. To deploy this paradigm for store search of Taobao, we address two key challenges: (i) stores are associated with complex store-level metadata and product-related information, which increases the need for high-quality labeled data; and (ii) user queries may either target a specific store or describe a product category to retrieve a diverse set of relevant stores, resulting in varying demands for retrieval precision and diversity. We propose GenStore, a GR framework tailored for e-commerce store search. For training, we synthesize high-quality pseudo-queries from store metadata and affiliated product details, pairing them with store identifiers to learn query-store mappings. During inference, we first classify each query’s intent, then apply entropy-gated contrastive decoding that performs constrained generation of store names by contrasting an expert model with a lightweight amateur model. An intent-specific similarity penalty further promotes diversity when appropriate. Extensive offline experiments and online A/B testing demonstrate that GenStore significantly enhances retrieval relevance compared to existing methods while preserving result diversity.