Covalent functionalization of single-walled carbon nanotubes (SWCNTs) with organic molecules results in red-shifted emissive states associated with sp3-defects in the tube lattice, which facilitate their improved optical functionality, including single-photon emission. The energy of the defect-based electronic excitations (excitons) depends on the molecular adducts, the configuration of the defect, and concentration of defects. Here we model the interactions between two sp3-defects placed at various distances in the (6,5) SWCNT using time-dependent density functional theory. Calculations reveal that these interactions conform to the effective model of J-aggregates for well-spaced defects (>2 nm), leading to a red-shifted and optically allowed (bright) lowest energy exciton. H-aggregate behavior is not observed for any defect orientations, which is beneficial for emission. The splitting between the lowest energy bright and optically forbidden (dark) excitons and the pristine excitonic band are controlled by the single-defect configurations and their axial separation. These findings enable a synthetic design strategy for SWCNTs with tunable near-infrared emission.