My wife's phone shows my apple ID. How can she delete my apple ID and add hers?

She needs to erase her iPhone, then set it up using her Apple ID. See how to erase an iPhone following the directions in this link --> What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Once the phone has been wiped, she would set it up as a new iPhone, signing in with her Apple ID, etc. As for apps and content you want to share between the devices, you can share the apps you've purchased by becoming the family organizer and use Family Sharing. This link explains how --> Family Sharing - Apple

Mauistrong wrote:

My wife uses same ID.

She has her own Apple ID

You provide conflicting information. Is she does not have her own ID already, do as I instruct so she can transfer as much as possible to a new account she needs to create. If she does have her own account already then erase her phone as Lobsterghost suggests and have her sign in with her account.

Make sure that each family member has a unique Apple ID as suggested in this support article --> Make sure that each family member has a unique Apple ID - Apple Support

This support article tells you how to create a new, non-child Apple ID = create an Apple Account. --> How to create a new Apple ID - Apple Support

Merging, splitting or transferring items between Apple accounts (IDs) is for the most part not officially supported. Read the links below for things you may need to do to transfer as much as is possible and to share some others.

Apps and media bought with one ID are permanently associated with that ID. Look into using Family Sharing to continue to be able to use items purchased with one Apple ID with other Apple IDs, and for some data sharing features.

- Family Sharing - What is Family Sharing? - Apple Support

- Set up Family Sharing - Set up Family Sharing - Apple Support

Share folders with iCloud Drive --> Share files and folders in iCloud Drive on iCloud.com - Apple Support

Read How to use Shared Albums in Photos on your iPhone, iPad, and Mac - Apple Support about how to share photos.

If you have signed into the first ID on a device then fortunately when you sign out of that ID, do not erase the device, then sign in with a different ID, it asks you in most cases if you wish to merge the data from the two IDs on your device (toggle the ones you want to on). Say yes and later delete individual items from the other ID that you do not want. Note, in How to save apps and progress on one Appl… - Apple Community a Community Specialist says, "you will not be able to transfer the meta data from one Apple ID to another. Once you switch to another Apple ID the information associated with the old Apple ID will be gone except for physical content on the device like photos and videos." Also turn off storage optimization before doing this. With Optimize Storage, smaller, space-saving photos and videos are kept on your device while all of your original, full-resolution versions are stored in iCloud. Make sure photo optimization is turned off. Manage your photo and video storage - Apple Support

Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac --> Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac - Apple Support

If another Apple ID is signed in you may need to enter the password for that ID to sign out of that ID first.

Click on this link to learn how to 'Sign in with your Apple ID' --> Sign in with your Apple ID - Apple Support

The problem is that you have setup her iPhone with your Apple ID. She needs to reset the device and set it up with her own Apple ID, not share yours. Apple IDs are not meant to be shared. If you are wanting to share content, then you can use Family Sharing for that. See this for creating the Apple ID, How to create a new Apple ID - Apple Support and then this for setting up Family Sharing. Set up Family Sharing - Apple Support

Before you dive into the not so easy task of setting up your wife's iPhone with a different Apple ID.....check on your wife's phone as follows:

Settings > Messages > Send & Receive

Make sure that the check mark appears only next to your wife's phone number. This might provide some temporary help.