It is possible for someone to lease real property they do not own. However, they must have some connection to the property to lawfully do so. In your example, if your landlord has his own lease with the property owner that permits subleases, then your landlord is a sublessor and you are a sublessee. Also, it could be that your landlord is either an agent (authorized by the landlord to enter into leases in the Agent's name) or trustee of the landlord. Now that you have discovered a difference exists between the owner name and your landlord's name, you should ask your landlord to explain why the records you saw list someone else as the owner of the property. Depending on the answer you would then next ask for the basis for their right to collect rent from you and/or collect rent on behalf of the landlord. Since there are many possible answers that are legitimate, until you get some explanation it is difficult to advise of what your rights are, or how your right to remain on the property could be affected.