Network slicing has emerged as a promising solution for end-to-end (E2E) resource management and orchestration, enabled by software-defined networking (SDN) and network function virtualization (NFV) technologies. In this paper, we investigate the dynamic E2E optical-wireless network slicing mapping problem in converged optical-wireless access networks. To address user data rate requirements in wireless networks and radio access network (RAN) slicing scheduling in optical networks, we first formulate an E2E optical-wireless network slicing mapping model with its associated constraints. Subsequently, to provide feasible solutions for real-world applications, we propose a dynamic E2E optical-wireless network slicing mapping (D-E2E-OW-NSM) algorithm based on deep reinforcement learning (DRL). To facilitate the decision-making process of the DRL agent, we decompose the intricate E2E optical-wireless network slicing request into several sub-requests, solving them one by one in turn. Simulation results demonstrate that our proposed method reduces the request blocking probability by up to 18.2% in a small-scale network and 11.3% in a large-scale network compared to baseline methods. Our analyses provide valuable insights into the modeling and design of efficient converged optical-wireless access networks for 5G and beyond.