Brillouin fiber lasers (BFLs) are a promising optical source technology for industrial and academic purposes that have experienced continuous progress in recent years. Currently, part of this development is focused on delivering laser solutions with low resonator loss, relatively low pump threshold, high efficiency, very small linewidth, and multi-wavelength architecture. In this perspective, this study employs an accurate numerical model based on an analytical solution to investigate the effect of the pump’s spectral linewidth on BFLs working both in single and cascaded multi-wavelength configurations. Output powers, thresholds, and the Stokes lines number simulated are analyzed here using a standard single-mode optical fiber as the Brillouin gain medium. The numerical results obtained not only allow identifying the regions of the pump’s spectral linewidth in which there is greater, moderate, or even no suppression of the stimulated Brillouin scattering inside the laser cavity but also provides a deep understanding of the internal dynamics of the BFLs cavities.