The rapid development of 5G technology and edge computing prompts emerging edge applications with heterogeneous requirements for network services with respect to latency, reliability, and throughput. Although content distribution networks (CDN) and edge computing proposals, such as multi-access edge computing (MEC), improve quality of service by deploying services close to end users at the edge, the session efficiency of service still is constrained by host name resolution, which also leads to quality degradation of service in the case of user mobility. In this article, we proposed a novel network architecture, Named Service Edge Network (NSEN), on the basis of DNS protocol. We enabled NSEN functionality in the MEC reference architecture and presented high-efficiency session models to satisfy the requirements of various edge applications and enhance the mobility support in distributed MEC environment. The simulation and experiment results demonstrate the NSEN-enabled MEC architecture can improve session efficiency of MEC services in 5G cellular networks in terms of latency and throughput.