What is the ruling on an employee renting his wife's private car through a car rental company – without the knowledge of the company he works for – in order to benefit from the rental value paid by the company, and is there any religious sin in doing so?

If the questioner is the one who will rent the car himself, then it is not permissible for him to rent his wife's car without the permission of his principal (the company), because he is an agent for it, and an agent should not rent from someone whose testimony is rejected for him, like his wife, due to the suspicion involved. However, if the company is the one that will handle the car rental, then there is no objection to renting his wife's car.