To achieve wind power utilization and low-carbon operation in multiple regional integrated energy systems (RIESs), an optimal allocation method for shared electricity-hydrogen storage (SEHS) is proposed, considering seasonal hydrogen storage and carbon emission penalties. First, by treating SEHS and all RIESs as the master and slave respectively, a bi-level game-based optimal allocation model of SEHS is established. Then, the carbon emissions of both SEHS and RIESs are calculated, and a carbon emission penalty price incorporating carbon tax is designed. Based on this, an optimal allocation model of SEHS that accounts for carbon emission reduction is reformulated. Finally, the presented model is transformed into a tractable mixed-integer linear programming formulation, and its effectiveness is validated through numerical case studies. The simulation results demonstrate that the proposed model can effectively address wind power imbalance over both long- and short-term timescales, while reducing the carbon emissions associated with RIES loads.