the Apple TV will not select in the Command Centre remote App.
The Apple TV box doesn’t get to select. Instead, the software remote in Control Center on iPhone will offer to work for a selected Apple TV box. I.e. the other way around.
Set up the Apple TV Remote on your iPhone or iPad - Apple Support
Both devices have to connect to the same home network, else they won’t be able to communicate with each other. E.g. iPhone on cellular-only will not work. E.g. If your Apple TV box isn’t connected to a home network yet, then the software remote will not work yet. Use a physical remote to help set that up first, if needed.
If the Apple TV box is a legacy model, then there may be further caveats.
If the Control Center widget detects multiple Apple TV boxes, then it it may default to an unintended different box.
What is the model Apple TV box?
Identify your Apple TV model - Apple Support
Find your Apple TV model number - Apple Support