Q: My iPhone 6 details shared on another iPhone 6

Hey Granette,

It sounds like you and your wife are using the same Apple ID on these two iPhones and that is causing the issues you describe. It is not adviseable to share an Apple ID for a number of reasons, not the least of which is this duplication. See this article - Use your own Apple ID for Family Sharing. Note that while the article title concerns Family Sharing, the info in it applies. Specifically -

Avoid sharing an Apple ID

If you share the same Apple ID with a family member for iTunes & App Store purchases, certain services will treat you as the same person. You may see these and other issues:

• Apple Music family membership: Instead of receiving your own membership with your own library, you’ll share a library and recommendations with the other family member.
• iTunes, iBooks, and App Store purchases: If Family Sharing is ever stopped, the owner of the shared Apple ID will keep all purchases. You might lose access to everything in the account, including purchases you initiated.
• Podcasts, iBooks, and iTunes U: Podcast episodes, bookmarks, and iTunes U courses might sync according to the other family member’s preferences or be accidentally deleted.

To see which Apple ID your family member is using to share, tap Settings > iCloud > Family and tap their name. Make sure that no one else is using your Apple ID to share content. 

To create another Apple ID for your wife (or for yourself) follow the directions here - Create and start using an Apple ID.

You woiuld then need to replace the Apple ID information on one of the phones with the new Apple ID. Use the information in the above article to sign in where needed. Specifically -

Sign in with your Apple ID

Use the same Apple ID and password every time you're asked to sign in to an Apple device or service. With your Apple ID, you can seamlessly:

• Sign in to iCloud to keep your personal content up to date on all your devices.
• Sign in to the iTunes, iBooks, and App Store to make purchases and access previous purchases.
• Sign in to iMessage and FaceTime with your Apple ID to talk and text with friends and family.
• Sign in to Game Center with your Apple ID to play games with friends and track your achievements.
• Sign in with your Apple ID when you set up a new device.

See a complete list of features and services that use your Apple ID.

Thanks for using Apple Support Communities.

Happy computing.