Hello timappleidfrozen,
Thank you for reaching out to Apple Support Communities, and we'll be happy to help in any way we can. We understand you're having issues with using another Apple ID with your iPhone. You will need to sign out of the old Apple ID and sign in with your new one. This goes over how to sign in with your Apple ID: Sign in with your Apple ID - Apple Support
"Sign in on your iPhone, iPad, or iPod touch
- Open the Settings app.
- Tap Sign in to your [device].
- Enter your Apple ID and password.
- If prompted, enter the six-digit verification code sent to your trusted device or phone number and complete sign in.
If you're already signed in to iCloud on the iPhone paired with your Apple Watch, you will automatically be signed in to that Apple ID. Learn more about how to set up and sign in to your Apple Watch. "
If there is a reason you are seeing that you are unable to log out of your old one, let us know so that we can help you out.
We hope this helps.
Cheers!