In the absence of a substantial ionosphere, solar wind protons dominate the plasma content within Mercury’s magnetosphere. However, Mercury is surrounded by a tenuous neutral exosphere composed primarily of sodium atoms, which can be continuously ionized. The production of sodium ions is concentrated on the dayside, and these ions can subsequently be transported to the magnetotail and flanks. MESSENGER spacecraft observations revealed dawn-dusk asymmetric distributions of sodium ions $Na^+$. In this study, we present a two-fluid MHD model that is coupled with an empirical sodium exosphere profile to investigate the circulation, distribution, and influence of $Na^+$ on global magnetospheric convection. Our findings indicate that the observed dawn-dusk asymmetries in $Na^+$ distributions are driven by the separation of $H^+$ and $Na^+$ flows, with the Hall-driven global convection preferentially transporting $Na^+$ ions to the morning sector.