Satellite communication networks promise to provide seamless global coverage in the 6G era. However, novel satellite networks face the challenges of high dynamics in terms of both communication and networking, which makes its design, emulation, deployment, and maintenance over-complicated. For these challenges, Digital Twin (DT) can establish a virtual replica of the physical system, providing a means of emulation, validation, prediction, and troubleshooting for the actual system whose benefits have been proven by many applications. In this work, we design a hierarchical digital twin network for satellite communication networks, which defines central-DT and edge-DT models that provide differentiated DT services such as communication DT and networking DT. Further, for the problem of model synchronization, we propose three approaches to improve the model synchronization efficiency, namely, dynamic DT migration, QoS-aware DT synchronization slice, and locator-identifier-isolation addressing mechanism. Simulation is conducted to validate the improvement of the proposed scheme, and provide proof of efficiency.