We study the $C=1$, $S=-2$, $I=0$ sector, where five excited $\Omega_c$ states have been recently observed by the LHCb Collaboration. We start from a recently developed unitarized baryon-meson model that takes, as bare baryon-meson interaction, an extended Weinberg-Tomozawa kernel consistent with both chiral and heavy-quark spin symmetries. This ${\rm SU(6)} \times {\rm HQSS}$ scheme leads to a successful description of the observed lowest-lying odd parity charmed $\Lambda_c$(2595) and $\Lambda_c$(2625) states, and bottomed $\Lambda_b$(5912) and $\Lambda_b$(5920) resonances. Within this model, five odd-parity $\Omega_c$ states are dynamically generated, but with masses below 3 GeV, not allowing for an identification with the observed LHCb resonances. We revise this model and explore two different scenarios for the renormalization scheme, that is, using a modified common energy scale to perform the subtractions or utilizing a common ultraviolet cutoff to render finite the ultraviolet divergent loop functions in all channels. In both cases, we show that some (at least three) of the dynamically generated states can be identified with the experimental $\Omega_c$, while having odd parity and $J=1/2$ or $J=3/2$. Two of these states turn out to be part of the same ${\rm SU(6)} \times {\rm HQSS}$ multiplets as the charmed and bottomed $\Lambda$ baryons.