Plasmon-molecule coupling has recently been attracted great research interest in material science and quantum optics with a multitude of potential applications. In this work, using the linear combination of atomic orbitals real-time-propagation rt-time dependent density functional theory (TDDFT) technique (LCAO-rt-TDDFT) and transition contribution maps, we investigate the optical and plasmonic features of a hybrid nanosystem comprising an elliptical-shaped metal nanoring (ENR) and a couple of benzene molecules (located in close proximity at both sides of the ENR short axis and/or long axis). We find that pristine ENR exhibits localized surface plasmon resonances (LSPRs) and plasmon-molecule coupling in hybrid nanosystems is highly sensitive to the location of the molecules. More specifically, when benzene molecules are placed at both sides of the ENR short axis, the dominant peak in the photoabsorption spectrum sustains its LSPR features with a significant enhancement in intensity. On the other hand, in an alternative situation where benzene molecules are placed at both sides of the ENR long axis, the dominant peak in the photoabsorption spectrum splits into three with diminishing LSPR features.