Hello Cblackledge41,
It sounds as though you're wanting to restore the iPhone to a backup that's associated to a different Apple ID. If you're restoring to an iCloud backup, that backup would be associated to that specific Apple ID and can't be transferred to a different account. If you're wanting to use a different Apple ID on the iPhone after it's been set up, you can follow the steps listed below to sign out of the Apple ID after the iPhone has been set up, then sign in to the desired Apple ID. Bear in mind, when restoring to a backup associated to a different Apple ID, the apps that are restored to the device would remain associated to that account. Any updates that become available for those apps, would require the password associated to the Apple ID used to download the apps originally to perform the update.
- Tap Settings.
- Tap [your name/Apple ID].
- Scroll down the screen, then tap Sign Out.
Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac
After signing out of the Apple ID, can follow the steps in the article below to sign in to the desired Apple ID.
Sign in with your Apple ID
Setting up the new iPhone as new can help avoid any issues with existing applications needing the password for the original Apple ID from needing to be entered. You can create a new Apple ID if one hasn't already been created, and use family sharing to share access to applications and other purchases. The following articles outlines more information about creating a new Apple ID and using Family Sharing.
How to create a new Apple ID
Set up Family Sharing
Take care!