Is the money a doctor receives from the hospital for assisting in kidney transplant operations, which may lead to donors receiving money through illicit means, considered unlawful gain?

There is no objection to the questioner's work, nor to the wages he receives, in principle. As for the donor receiving money, if it is an unconditional gift or reward, it is not forbidden. However, if it is conditional, then it is the sale of organs, which is religiously forbidden and legally criminalized. If the doctor knows that the kidney has been sold, he is not permitted to perform the surgery, as it constitutes assisting in what is forbidden. However, in cases of doubt, the original ruling of permissibility remains, for what is unknown is as if it does not exist. In cases of necessity, if it is permissible for the patient to buy a kidney, it is permissible for the doctor to perform the operation.