Is it permissible, Islamically, for me to rent a house and live in another, knowing that the owner is the same for both houses, and that the partnership does not entail any additional costs?

It is not permissible to inform the company that you reside in a certain accommodation while you live elsewhere, due to the forbidden lie involved. The sin is compounded if the company stipulates specific characteristics for the accommodation, for in this case, the sin of deception is added to the lie.