With the growing popularity of virtual character platforms like Character.AI, users are increasingly turning to role-playing agents for emotional support in daily life. Yet existing research mainly focuses on character consistency in fictional or game-based scenarios, overlooking user-centered interactions such as companionship and psychological support. To bridge this gap, we propose Emotionally Supportive Role-Playing (ESRP), a framework designed to align role-playing with real-world user scenarios and emotional needs. We focus on typical users of these platforms, i.e., anime enthusiasts—including students, office workers, freelancers, and self-employed individuals—and design scenario-based questions that reflect their everyday struggles such as work stress and social loneliness. Through a two-round data collection involving 40 anime fans and 10 Large Language Models (LLMs), we build ChatAnime: the first ESRP dataset with 2,400 human-written and 24,000 LLM-generated responses, supported by over 132,000 fine-grained human annotations. We also provide the ESRP evaluation framework featuring 9 fine-grained metrics across three dimensions: basic dialogue, role-playing and emotional support, along with an overall metric for diversity. Experimental results under our evaluation setting show that top-performing LLMs surpass anime fans in role-playing and emotional support, while humans still lead in diversity.