Electron-phonon coupling in graphene is currently a subject of intense research. Theoretically, the coupling constants are usually calculated using density-functional theory (DFT), where the exchange (Fock) term is treated in the local density approximation, or the generalized gradient approximation. In this work we consider mutual effect of weak electron-phonon and strong Coulomb interactions on each other by summing up leading logarithmic corrections via the renormalization group approach, which goes beyond Hartree-Fock approximation. We find that coupling constants to different phonon modes are renormalized differently, which explains the experimentally observed intensities of Raman peaks.