The emission of Cr-doped Sc2O3 (space group Ia3̅, No. 206) phosphor features a broad band in NIR-I (700-1000 nm) and another in NIR-II (1000-1700 nm), which is significant for spectral analysis and medical applications. Although Sc2O3 has two 6-coordinated Sc sites─the nearly octahedral site with S6 point-group symmetry (S6 site) and the highly distorted site with C2 symmetry (C2 site)─the origin of the dual-band emission remains widely debated. In this study, we performed first-principles calculations to investigate the properties of Cr and Ni dopants in Sc2O3, including preference in site occupation, valence state, ligand field strength, Stokes shift, and line shape. Our calibrated calculations conclusively determined that the NIR-I emission peak at 840 nm is due to Cr3+ at the S6 site. However, the broad NIR-II emission peaking at around 1280 nm cannot be attributed to Crq (q = +2, +3, +4) at either site, suggesting the presence of possible trace impurities and phases. Ni2+ ions at octahedral sites exhibit a narrow peak width and long lifetime, which contradict reported experimental observations. The Cr4+ ions at a tetrahedral site, similar to that in the phase of Sc2O3 with the space group Pna21 (No. 33), show the most consistent line shape and emission decay rates with experimental data. A systematic first-principles approach incorporating the line shape calculation can be useful to resolve the issues in identifying luminescent centers in systems involving intrinsic defects and dopants.