Evaluating Retrieval-Augmented Generation (RAG) systems, especially in domain-specific contexts, requires benchmarks that address the distinctive requirements of the applicative scenario. Since real data can be hard to obtain, a common strategy is to use LLM-based methods to generate synthetic data. Existing solutions are general purpose: given a document, they generate a question to build a Q&A pair. However, although the generated questions can be individually good, they are typically not diverse enough to reasonably cover the different ways real end-users can interact with the RAG system. We introduce here DataMorgana, a tool for generating highly customizable and diverse synthetic Q&A benchmarks tailored to RAG applications. DataMorgana enables detailed configurations of user and question categories and provides control over their distribution within the benchmark. It uses a lightweight two-stage process, ensuring efficiency and fast iterations, while generating benchmarks that reflect the expected traffic. We conduct a thorough line of experiments, showing quantitatively and qualitatively that DataMorgana surpasses existing tools and approaches in producing lexically, syntactically, and semantically diverse question sets across domain-specific and general-knowledge corpora. DataMorgana will be made available to selected teams in the research community, as first beta testers, in the context of the upcoming SIGIR'2025 LiveRAG challenge to be announced in early February 2025.