Modifications in dielectric properties of palladium upon absorption of hydrogen are investigated theoretically in the low-energy (0-2 eV) region. The calculations were performed with full inclusion of the electronic band structure obtained within a self-consistent pseudopotential approach. In particular, we trace the evolution of the acoustic-like plasmon (AP) found previously in clean Pd with increasing hydrogen concentration. It exists in PdHx up to the hydrogen content x corresponding to the complete filling of the 4d Pd-derived energy bands because of the presence of two kinds of carriers at the Fermi surface. At higher H concentration the AP disappears since only one kind of carrier within the sp-like energy band exists at the Fermi level. Additionally, we investigate the spatial distribution inside the crystal of a potential caused by a time-dependent external perturbation and observe drastic modifications in the screening properties in the PdHx systems with energy and with hydrogen concentration.