The interaction of the solar wind (SW) with the magnetic field of Mercury is investigated by means of a three dimensional parallelized multispecies hybrid model. A comparison between two mathematical representations of Mercury's intrinsic magnetic field is studied. The first model is an Offset Dipole (OD) having the offset and dipolar moment reported by Anderson et al. (2011). The second model is a combination of a Dipole and a Quadrupole (DQ), the total field is fitted to the offset dipolar field, for northern latitudes greater than 50°. Simulations reproduce the features which characterize Mercury's interaction with the SW, encompassing the Bow Shock (BS), the magnetosheath, the magnetotail, the “cusps” region and the neutral current sheet. Global hybrid simulations of the Hermean magnetosphere run for the OD and DQ models demonstrate that the southern parts of the magnetospheres produced by the OD and DQ models differ greatly in topology and volume meanwhile their northern parts‐are quite similar. In particular the DQ model exhibits a dome of closed field lines around the south pole in contrast to the OD. Without further information on the intrinsic magnetic field of the planet in the southern region which should be provided by BepiColombo after year 2020, we can only speculate on the influence of the different magnetic topologies on the magnetospheric dynamics.