In this paper we treat the 3D stochastic incompressible generalized rotating magnetohydrodynamics equations. By using Littlewood–Paley decomposition and Itô integral, we establish the global well-posedness result for small initial data $(u_0, b_0)$ belonging in the critical Fourier–Besov–Morrey spaces $\mathcal{F}N^{\frac{5}{2}-\frac{3}{q}+\frac{2}{\lambda}}_{2,\lambda,q}(\mathbb{R}^3)$.
In addition, the proof of local existence is also founded on \emph{a priori} estimates of the stochastic parabolic equation and the iterative contraction method.