Hello Larry Lipner,
An unfamiliar Xbox gamertag does not necessarily mean you’re signed in to someone else’s account. Xbox may have assigned a gamertag when your profile was created.
Since reinstalling Solitaire did not help, could you check one thing first? In Microsoft Store, select your profile picture and check whether the signed-in account is the one that purchased Solitaire Premium. Then check whether that same account shows an active Premium subscription in Services & subscriptions.
If those match, please let me know whether Solitaire still shows the unfamiliar gamertag or asks you to sign in. That will help separate an account mismatch from a problem recognizing your subscription. Please don’t post your email address or payment details here.