Is it permissible to be paid for covering the emergency department in a hospital, knowing that the doctor's name is not listed in the official records and he receives payment from a colleague?

Your taking another doctor's name and attending in his place to collect the fee is considered forgery and forbidden deception, because of the Almighty's saying: "So shun false words." And the supervisor's cooperation with you in this is cooperation in forbidden sin. You must seek forgiveness for what you have done and return the amount you took to the hospital if possible; otherwise, give it to the poor and needy.