change a phones name on account

If 13 years old or older.

Apple ID - create a new.      

Apple ID – Create         

If under 13 years old, you will need to set up Family Sharing to create an ID.

Family Sharing and Apple ID for your child.      

Family Sharing.         

Family Sharing - Set up.        

When changing to the new ID, 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 and/or in Photos/Preferences/iCloud. Then make sure full resolution photos are on the device/computer. 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. See Winston Churchill's response in the below discussion. Also set up Family Sharing between the IDs to keep access to your apps/purchases. 

How to switch Apple IDs on your iPhone or iPad.      

How to transfer all files from one iCloud account to another.        

What to do after you change your Apple ID or password - Apple Support.     

At the risk of answering a question not asked, you’d be in much better shape creating a separate AppleID for your daughter now.

I’ts MUCH more secure for BOTH of you, it provides great parental management tools, and most importantly; it eliminates “extricating” her from your account once she’s grown up.

(Something which is difficult and messy)

See article below for details:

https://www.apple.com/family-sharing/