The spin character of the states at the top of the valence band in doped La(2-x)Sr(x)CuO(4) (x=0.03, 0.07, 0.15, 0.22, and 0.30) has been investigated using spin-polarized resonant photoemission. A clear Zhang-Rice singlet (ZRS) is observed at all doping levels. Its stability and polarization are preserved as a function of doping, suggesting that the concept of the ZRS can be used across a wide doping range and up to the metallic nonsuperconducting overdoped regime. The results are significant for theoretical models that use the ZRS approximation and for the understanding of the peculiar interplay between the ZRS and the remaining localized spins.