Based on the atomistic tight-binding theory (TB) and a configuration interaction (CI) description, the electron-hole exchange interaction in the morphological transformation of CdSe/ZnS core/shell nanodisk to CdSe/ZnS core/shell nanorod is described with the aim of understanding the impact of the structural shapes on the change of the electron-hole exchange interaction. Normally, the ground hole states confined in typical CdSe/ZnS core/shell nanocrystals are of heavy hole-like character. However, the atomistic tight-binding theory shows that a transition of the ground hole states from heavy hole-like to light hole-like contribution with the increasing aspect ratios of the CdSe/ZnS core/shell nanostructures is recognized. According to the change in the ground-state hole characters, the electron-hole exchange interaction is also significantly altered. To do so, optical band gaps, ground-state electron character, ground-state hole character, oscillation strengths, ground-state coulomb energies, ground-state exchange energies, and dark-bright (DB) excitonic splitting (stoke shift) are numerically demonstrated. These atomistic computations obviously show the sensitivity with the aspect ratios. Finally, the alteration in the hole character has a prominent effect on dark-bright (DB) excitonic splitting.