To develop an understanding of the photochromic effect in rare-earth metal oxyhydride thin films (REH3-2xOx, here RE = Y), we explore the aliovalent doping of the RE cation. We prepared Ca-doped yttrium oxyhydride thin films ((CazY1-z)HxOy) by reactive magnetron cosputtering with Ca doping concentrations between 0 and 36 at. %. All of the films are semiconductors with a constant optical band gap for Ca content below 15%, while the band gap expands for compositions above 15%. Ca doping affects the photochromic properties, resulting in (1) a lower photochromic contrast, likely due to a lower H- concentration, and (2) a faster bleaching speed, caused by a higher pre-exponential factor. Overall, these results point to the importance of the H- concentration for the formation of a "darkened"phase and the local rearrangement of these H- for the kinetics of the process.