If I understand your inquiry correctly, you're looking for the name of the dead German soldier that your father took the pistol from. Seems like quite a grisly task to me and, I must say, in all my years of collecting, I have only seen one instance where a wartime German pistol was connected to its original owner. To my knowledge, no lists of issued German wartime weapons has surfaced thus far so I think it is unlikely that you will ever discover the dead German's name.
However, you may be able to link your father's unit at the time (from the pistol "Capture Paper" required to bring it back to the U.S.) and German units associated with it in battle. That might bring you somewhat closer to an answer.