It makes a difference in who gets to stay longer term. If the LL rented to only one of them (example, before, the marriage occured) lease terms may not require him to continue to rent to a "third party" once the LLs tenant has moved out. A property owner entres into an agreement to provide THEIR property to the tenant for whom they have run the credit checks, verified employment or income, etc. A LL is not necessarilly obligated to allow a third party to stay alone in a rental, when the rental agreement is NOT with the occupant. So it's something that should be considered in deciding "who will stay and who will go"