Berry monopoles are point degeneracies in parameter space where the Berry curvature emanates radially, analogous to magnetic monopoles. Here, we report the adiabatic merging and splitting of Berry monopoles in a bilayer photonic crystal slab combining one genuine and one synthetic momentum. Two monopoles approach, merge, and split within this hybrid parameter space. The process is described by an effective coupled-mode model and confirmed by full-wave simulations. We further propose a scheme to experimentally probe the Berry monopole merging and splitting by monitoring the evolution of chiral edge states localized at the interface between two topological phases with inverted band structures.