My family is now receiving my text messages. How do I turn this feature off?

It sounds as though you're sharing an Apple ID with other family members. Apple IDs are intended to be used by one person only. You each need your own Apple ID. If you want to share content, set up Family Sharing.

Set up Family Sharing - Apple Support

There may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos. Then make sure full resolution photos are on the device. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. Also set up Family Sharing to keep access to your apps. Also see Winston Churchill's response in the below discussion

Apple ID – Create

How to transfer all files from one iCloud account to another

Apple ID email address or password - What to do after you change

Family Sharing - Use your own Apple ID for Family Sharing

Family Sharing -What types of content can I share?

Family Sharing - If you don‘t see your family‘s shared content

Family Sharing - Ask to Buy

Family Sharing - purchases and payments

Family Sharing - Hide and unhide music, movies, TV shows, audiobooks, and books

Family Sharing – share iCloud Storage

Family Sharing - Share an iCloud storage plan with your family

Family Sharing and location

Family Sharing and Apple ID for your child