wife's iPhone 8+ shows my name

NJEsto wrote:

My wife and I share one Apple account under my name

Stop doing this immediately. Each unique person needs her/his own Apple ID.

• Create an Apple ID for your wife. How to create a new Apple ID - Apple Support
• Thoroughly cleanse her iPhone as follows. What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support
• She can now "move in" to her new-like iPhone. She should not introduce any material owned by your Apple ID.
• You and your wife may use Family Sharing should you choose to do so. Set up Family Sharing - Apple Support

Regarding apps and iTunes stuff, you may use Purchase Sharing.

What is Family Sharing? - Apple Support

You may also institute a Family calendar.

Regarding contacts, you may share those one at a time. When viewing a contact, you will find "Share Contact" as an option.

You’re welcome.

Enjoy your IPhones.