Energy storage (ES) units are vital for the reliable and economical operation of the power system with a high penetration of renewable distributed generators (DGs). Due to ES’s high investment costs and long payback period, energy management with shared ESs becomes a suitable choice for the demand side. This work investigates the sharing mechanism of ES units for low-voltage (LV) energy prosumer (EP) communities, in which energy interactions of multiple styles among the EPs are enabled, and the aggregated ES dispatch center (AESDC) is established as a special energy service provider to facilitate the scheduling and marketing mechanism. A shared ES operation framework considering multiple EP communities is established, in which both the energy scheduling and cost allocation methods are studied. Then a shared ES model and energy marketing scheme for multiple communities based on the leader–follower game is proposed. The Karush–Kuhn–Tucker (KKT) condition is used to transform the double-layer model into a single-layer model, and then the large M method and PSO-HS algorithm are used to solve it, which improves convergence features in both speed and performance. On this basis, a cost allocation strategy based on the Owen value method is proposed to resolve the issues of benefit distribution fairness and user privacy under current situations. A case study simulation is carried out, and the results show that, with the ES scheduling strategy shared by multiple renewable communities in the leader–follower game, the energy cost is reduced significantly, and all communities acquire benefits from shared ES operators and aggregated ES dispatch centers, which verifies the advantageous and economical features of the proposed framework and strategy. With the cost allocation strategy based on the Owen value method, the distribution results are rational and equitable both for the groups and individuals among the multiple EP communities. Comparing it with other algorithms, the presented PSO-HS algorithm demonstrates better features in computing speed and convergence. Therefore, the proposed mechanism can be implemented in multiple scenarios on the demand side.