Large Language Models (LLMs) often suffer from hallucinations and outdated or incomplete knowledge. Retrieval-Augmented Generation (RAG) is proposed to address these issues by integrating external knowledge like that in knowledge graphs (KGs) into LLMs. However, leveraging private KGs in RAG systems poses significant privacy risks due to the black-box nature of LLMs and potential insecure data transmission. In this paper, we investigate the privacy-protected RAG scenario for the first time, where entities in KGs are anonymous for LLMs, thus preventing them from accessing entity semantics. Due to the loss of semantics of entities, previous RAG systems cannot retrieve question-relevant knowledge from KGs by matching questions with the meaningless identifiers of anonymous entities. To realize an effective RAG system in this scenario, two key challenges must be addressed: (1) How can anonymous entities be converted into retrievable information? (2) How to retrieve question-relevant anonymous entities? To address these challenges, we propose a novel Abstraction Reasoning on Graph (ARoG) framework including relation-centric abstraction and structure-oriented abstraction strategies. For challenge (1), the first strategy abstracts entities into high-level concepts by dynamically capturing the semantics of their adjacent relations. Hence, it supplements meaningful semantics which can further support the retrieval process. For challenge (2), the second strategy transforms unstructured natural language questions into structured abstract concept paths. These paths can be more effectively aligned with the abstracted concepts in KGs, thereby improving retrieval performance. In addition to guiding LLMs to effectively retrieve knowledge from KGs, these abstraction strategies also strictly protect privacy from being exposed to LLMs. Experiments on three datasets demonstrate that ARoG achieves strong performance and privacy-robustness, establishing a new practical direction for privacy-protected RAG systems.