How to separate my Apple ID from my childs

Apple IDs are neither merged nor combined so there's nothing to separate.

If you created a child Apple ID it is and remains separate since creation. It is not tied to your own Apple ID in any way, but while being under the age of 13, it must be part of a Family Sharing group.

Once it ages past 13, then it can be removed from Family Sharing and exist on its own.

What exactly are you trying to accomplish?

Music libraries, purchases, and apps are separate, but can be shared. If you are paying for her purchases and no longer want to, you can turn off purchase sharing in Family Sharing or remove her Apple ID from Family Sharing.

If something else is going on, then please explain what that is.

click here ➜ Remove someone from Family Sharing - Apple Support

That's probably because of how you have her number set up in your contacts.

If her number is under your own contact or a contact with your name, it will be shown as coming from you.

Check the contacts app for her number and make sure her information is correctly added to the contact the number or email address is in.

Also, check settings on her device, and make sure your Apple ID is not logged in for Messages and your number or Apple ID is not added to Settings ➜ Messages