The Apple TV app relies on individual Apple Accounts to keep things separate.
You would need to create an Apple Account for the person, and have them log into it on the Apple TV app. Then switch to the relevant account from Settings when needed.
click here ➜ Add user profiles to the Apple TV app - Apple Support
and here ➜ Use the sidebar to navigate the Apple TV app - Apple Support
Do note, if you want them to access content from an Apple TV+ subscription and any channels you may have added, you will need to enable Family Sharing.
click here ➜ How to set up Family Sharing on your iPhone, iPad, or Mac - Apple Support