We first determine the most stable adsorption site (top or hollow) for single Co atoms on MgO(001) performing plane-wave DFT calculations on periodic models. To assess different DFT-based methods, we compare binding energies and magnetic anisotropy energy predictions across multiple levels of theory, including the generalized gradient approximation (GGA), hybrid-GGA, DFT+U , and beyond-DFT random-phase approximation (RPA).