Raman scattering can occur at any frequency with a constant frequency of incident light. Fluorescence is tied to a different wavelength or frequency, that is, a shift will occur if the excitation wavelength is different. In addition, fluorescence signals can vary in a certain range. To reduce the effect of fluorescence on the Raman spectra, long-wave excitation sources should be used.
There are various origins of fluorescences and luminescences in Raman spectra. The case that the material itself is luminescent has been discussed sufficiently by Yuri Mirgorod . There is another possibility: if your spectrometer is getting older there may be damages in the optical fibers or mirrors may have taken up some oxygen over time. Especially if your sample is highly reflective so that a high radiation intensity enters the system this may cause luminescences on the optical path between sample and detector. This can be reduced by tilting the sample; at some point, optical fibers may have to be exchanged.