Robots are increasingly deployed in dynamic and crowded environments, such as urban areas and shopping malls, where efficient and robust navigation is crucial. Traditional risk-based motion planning algorithms face challenges in such scenarios due to the lack of a well-defined search region, leading to inefficient exploration in irrelevant areas. While bi-directional and multi-directional search strategies can improve efficiency, they still result in significant unnecessary exploration. This article introduces the Neural Adaptive Multi-directional Risk-based Rapidly-exploring Random Tree (NAMR-RRT) to address these limitations. NAMR-RRT integrates neural network-generated heuristic regions to dynamically guide the exploration process, continuously refining the heuristic region and sampling rates during the planning process. This adaptive feature significantly enhances performance compared to neural-based methods with fixed heuristic regions and sampling rates. NAMR-RRT improves planning efficiency, reduces trajectory length, and ensures higher success by focusing the search on promising areas and continuously adjusting to environments. The experiment results from both simulations and real-world applications demonstrate the robustness and effectiveness of our proposed method in navigating dynamic environments. A website about this work is available at https://sites.google.com/view/namr-rrt.