How do I set up a new mail box for a unit I added to my house?

[Zeke Sherrod]

Hello, my name is Zeke. My wife and I recently bought a single family home and installed a full apartment unit in the basement. We have a friend that has done some property management for his family's rental real estate business. He told us that after you have installed the physical mailbox you just need to go to the post office and ask them to setup a unit B mailbox for you existing address. When we tried this they told us that we would have apply for a new address with the city. Does anyone have any experience, guidance, or resources you would recommend? Since the postal service is federal I would expect it to matter but we are in Knoxville, TN.  

Thanks !