In resonant inelastic light scattering experiments on two-dimensional hole systems in GaAs-Al(x)Ga(1-x)As single quantum wells we find evidence for the strongly anisotropic spin-split hole dispersion at finite in-plane momenta. In all our samples we detect a low-energy spin-density excitation of a few meV, stemming from excitation of holes of the spin-split ground state. The detailed spectral shape of the excitation depends sensitively on the orientations of the linear light polarizations with respect to the in-plane crystal axes. In particular, we observe a doublet structure, which is most pronounced if the polarization of the incident light is parallel to the [110] in-plane direction. Theoretical calculations of the Raman spectra based on a multiband k · p approach confirm that the observed doublet structure is due to the anisotropic spin-split hole dispersion.