Rotationally symmetric micro-cavities with disk, ring or toroidal shape displaying whispering gallery modes (WGMs) play an essential role in modern-day photonics. Due to the reduced symmetry of such resonators compared to spheres, an exact analytical model yielding WGMs as solutions does not exist. The established WGM classification scheme based on approximated analytical solutions is generally useful but neglects a possible interaction between the different modes. In this paper, we assess the limitation of the validity of this established classification based on extensive finite element method (FEM) simulations. We investigate respective mode couplings as well as underlying selection rules based on avoided crossings of the modes' resonance wavelengths. We propose conserved mode properties solely based on true symmetries of the underlying refractive-index distribution and deduce a novel WGM classification scheme.