If 100 people issue the same search query, they may have 100 different goals. While existing work on user-centric AI evaluation highlights the importance of aligning systems with fine-grained user intents, current search evaluation methods struggle to represent and assess this diversity. We introduce BloomIntent, a user-centric search evaluation method that uses user intents as the evaluation unit. BloomIntent first generates a set of plausible, fine-grained search intents grounded on taxonomies of user attributes and information-seeking intent types. Then, BloomIntent provides an automated evaluation of search results against each intent powered by large language models. To support practical analysis, BloomIntent clusters semantically similar intents and summarizes evaluation outcomes in a structured interface. With three technical evaluations, we showed that BloomIntent generated fine-grained, evaluable, and realistic intents and produced scalable assessments of intent-level satisfaction that achieved 72% agreement with expert evaluators. In a case study (N=4), we showed that BloomIntent supported search specialists in identifying intents for ambiguous queries, uncovering underserved user needs, and discovering actionable insights for improving search experiences. By shifting from query-level to intent-level evaluation, BloomIntent reimagines how search systems can be assessed -- not only for performance but for their ability to serve a multitude of user goals.