We study the dynamical dielectric function of a two-dimensional hole gas, exemplified on [001] GaAs and InAs quantum wells, within the Luttinger model extended to the two lowest subbands including bulk and structure inversion asymmetric terms. The plasmon dispersion shows a pronounced anisotropy for GaAs-and InAs-based systems. In GaAs this leads to a suppression of plasmons due to Landau damping in some orientations. Due to the large Rashba contribution in InAs, the lifetime of plasmons can be controlled by changing the electric field. This effect is potentially useful in plasmon field effect transistors as previously proposed for electron gases. DOI: 10.1103/PhysRevB.87.085321