Recent spectroscopic studies have revealed the appearance of multiple low-energy peaks in the fluorescence of single-walled carbon nanotubes (SWCNTs) upon their covalent functionalization by aryl groups. The photophysical nature of these low energy optical bands is of significant interest in the quest to understand their appearance and to achieve their precise control via chemical modification of SWCNTs. This theoretical study explains the specific energy dependence of emission features introduced in chemically functionalized (6,5) SWCNTs with aryl bromides at different conformations and in various dielectric media. Calculations using density functional theory (DFT) and time dependent DFT (TD-DFT) show that the specific isomer geometry - the relative position of functional groups on the carbon-ring of the nanotube - is critical for controlling the energies and intensities of optical transitions introduced by functionalization, while the dielectric environment and the chemical composition of functional groups play less significant roles. The predominant effects on optical properties as a result of functionalization conformation are rationalized by exciton localization on the surface of the SWCNT near the dopant sp3-defect but not onto the functional group itself.