Motivated by recent experimental observations of charmonium(-like) states, we investigate their interpretation as conventional charmonium states within the framework of relativized quark potential model. We find a consistent description of the updated masses of charmonium, bottomonium and some selected charmed mesons, then systematically compute open-charm strong decay widths and electromagnetic transition widths for radially excited charmonium states up to $n=5$. The numerical results show significantly improved agreement with experimental masses and widths. Notably, the newly-observed ${\chi }_{c1}(4010)$ and ${\chi }_{c1}(4274)$ are tentatively associated with the ${\chi }_{c1}(2P)$ and ${\chi }_{c1}(3P)$ respectively, while the ${\chi }_{c0}(4500)$ and ${\chi }_{c0}(4700)$ are interpreted as the ${\chi }_{c0}(4P)$ and ${\chi }_{c0}(5P)$ states. For the controversial ${\chi }_{c1}(3872)$ state, we suggest its potential connection to ${\chi }_{c1}(4010)$, as a two-pole structure due to the ${\chi }_{c1}(2P)$ coupling to $D{\bar{D}}^{*}$ channels. Intriguingly, the predicted mass of ${\chi }_{c0}(2P)$ is about 3851 MeV, diverging from the original estimate of $3916$ MeV in the Godfrey and Isgur’s work but consistent with non-relativistic potential model predictions. This calculation might provide more insight to the future experimental investigation of charmonium(-like) states.