The real-space topological domain structure has been receiving increasing interests recent years and its dynamics remains to be explored if any potential application becomes possible. We have investigated carefully the real-space topological domain structures of hexagonal RMnO3 manganites from various aspects, based on the phenomenological Ginzburg-Landau theory. First, the in-plane and out-of-plane stiffness anisotropies have been revealed to play a substantial role in controlling the domain structure. Second, we disclose in details of the dynamic response of the domain structure on external electric field. The present work provides a comprehensive understanding of the topological domain pattern evolution in hexagonal manganites, addressing the significance of the vortex-antivortex topology and proposing possible modulation of the domain structure by strain engineering and field stimuli.