We present a systematic Raman study over a range of excitation energies of arc discharge single-walled carbon nanotubes (SWCNTs) covalently functionalized according to two processes, esterification and reductive alkylation. The SWCNTs are characterized by resonance Raman spectroscopy at each step of the functionalization process, showing changes in radial breathing mode frequencies and transition energies for both semiconducting and metallic tubes. Particular attention is given to a family of tubes clearly identified in the Kataura plot for which we continuously tune the excitation energy from 704 to 752 nm. This allows us to quantify the energy shift occurring in the spacing of the van Hove singularities. We demonstrate that, independently of the functionalization technique, the type of chain covalently bound to the tubes plays an important role, notably when oxygen atoms lie close to the tubes, inducing a larger shift in transition energy as compared to that of other carbonaceous chains. The study shows the complexity of interpreting Raman data and suggests many interpretations in the literature may need to be revisited.