Thx a lot bogdanw, it worked fine!Nothing, it should be there. You could try to make copies of ~/Library/Preferences/com.apple.ncprefs.plist and ~/Library/Preferences/com.apple.TV.plist, delete the originals and log out or restart. The two preference files for the Notification Center and Apple TV should be recreated, hopefully correctly.
Unfortunately, when I opened another app (here Telegram) a few hours later, then this app appeared in the Notification Center, but the app TV had disappeared in that list. So I applied your recommended procedure again. Now all seems fine, hopefully for longer...