We study oxygen K-edge x-ray absorption spectroscopy (XAS) and investigate the validity of the Zhang-Rice singlet (ZRS) picture in overdoped cuprate superconductors. Using large-scale exact diagonalization of the three-orbital Hubbard model, we observe the effect of strong correlations manifesting in a dynamical spectral weight transfer from the upper Hubbard band to the ZRS band. The quantitative agreement between theory and experiment highlights an additional spectral weight reshuffling due to core-hole interaction. Our results confirm the important correlated nature of the cuprates and elucidate the changing orbital character of the low-energy quasiparticles, but also demonstrate the continued relevance of the ZRS even in the overdoped region.