Raman spectroscopy is frequently used to identify composition, structure and layer thickness of 2D materials. Here, we describe an efficient first-principles workflow for calculating resonant first-order Raman spectra of solids within third-order perturbation theory employing a localized atomic orbital basis set. The method is used to obtain the Raman spectra of 733 different monolayers selected from the Computational 2D Materials Database (C2DB). We benchmark the computational scheme against available experimental data for 15 known monolayers. Furthermore, we propose an automatic procedure for identifying a material based on an input experimental Raman spectrum and apply it to the cases of MoS2 (H-phase) and WTe2 (T′-phase). The Raman spectra of all materials at different excitation frequencies and polarization configurations are freely available from the C2DB. Our comprehensive and easily accessible library of ab initio Raman spectra should be valuable for both theoreticians and experimentalists in the field of 2D materials.