Hello about78,
Thanks for reaching out to Apple Support Communities. It sounds like you're having an issue with a Medical ID showing on your wife's iPhone. We're happy to provide some information to assist.
We recommend checking to see if you can edit the information using the steps here: Set up your Medical ID in the Health app on your iPhone
The article here can also assist with checking and editing the settings for your Medical ID: Fill out your Health Details and Medical ID in Health on iPhone
You'll also want to make sure you're not sharing an Apple ID. If you'd like to share purchases check out the options for Family Sharing here: Use your own Apple ID for Family Sharing
If you continue to have any issues, reach out to Apple Support directly here: Contact Apple Support
Best!