If the users watch the same content together, then either account can be used, and the other subscription can be canceled.
If you watch different content, or the some same content at different times, then you may be better off using Family Sharing, sharing the subscription, but through individual Apple ID accounts, to keep the watch histories etc. separate. Even then, one of the subscriptions can be canceled.
The Apple TV+ subscription is linked to the Apple ID account as set for the Store.
The account for iCloud services is separate, but will be the same account for many users. The account for iCloud services is also used for HomeKit, Photos, color calibration, virtual keyboard on iPhone, and a few other services.
However, I’m not sure which we’re using as the account name in the tv app settings is an iCloud account I don’t remember making and it doesn’t belong to either of our Apple IDs.
The modern Apple TV box lists a default user, and optionally more users, which can be switched between.
The default user would have an account for Store services, iCloud services, and Game Center.
An additional user would have an account for Store services, iCloud services, and Game Center.
(There would be a separate account for Home Sharing.)
The accounts would have the form of an email address, which may use the @icloud.com, or something different.
The accounts for one user may all be the same, and that will for many users. Exceptions are allowed, but such division is mostly historical. Also these sign-ins can be optional; i.e. sign in for one service, but not the other.
Accounts for iCloud services doesn’t have to be like @icloud.com. Accounts like @icloud.com can be for non-iCloud services use. All this is independent.
If someone else has set up this Apple TV box, then the mystery account might be from that person? Possibly a former owner? It would have been better to reset before taking over a device from someone else.
Where exactly is that listed?
If neither of you know the Apple ID, then it will remain a mystery. I don’t think that anyone else can tell you. Perhaps try sending an email message to it?