Is it permissible to house a third person in a rented home without the owner's knowledge, especially when a specific rent amount was agreed upon for the tenant residing alone, and a different amount for him residing with his friend?

If you and your friend rent a house and possess the usufruct of dwelling in it with all its facilities, then you may rent it to others, or rent part of it, as long as it does not cause damage to the house exceeding the damage from your own dwelling, even if the landlord is unaware of it. For the rent is ownership of the usufruct, and the tenant is permitted to dispose of it as he wishes, provided that the new tenant takes his place in benefiting from it.