With the rapid development of 5G/6G mobile communication technology, the application of satellite communication in wide-area coverage and remote area communication is getting more and more attention. The current 5G core network adopts a centralized approach to register and discover services with a network repository function (NRF). However, in the complex scenarios of 6G ultralarge scale multi-access, especially in satellite scenarios, it will trigger problems such as single point failure, performance bottleneck, and insufficient scalability, which will lead to the paralysis of the whole core network. In order to cope with the challenges of high latency and network instability in satellite scenarios, we propose a distributed service registration and discovery mechanism, which stores and discovers the service registration information quickly and efficiently through an improved consistent hash algorithm to enhance the reliability and efficiency of the core network. We have conducted large-scale simulations of the distributed service registration and discovery method on the Mininet platform. The evaluation results show that our proposed method disperses data and requests to different nodes and shares the load of the central node, which avoids the occurrence of single point failure. Meanwhile, the method reduces the service registration and discovery time during concurrent requests from multiple nodes, which effectively solves the performance bottleneck problem.