Apple ID

If you want separate phones (contacts, mail, photos etc) you need to create new Apple ID.

How to create a new Apple ID - Apple Support

If you want share some resources etc, you need to setup Family Sharing (with that new Apple ID)

Family Sharing - Apple

Set up Family Sharing – Apple Support (AU)

Create an Apple ID for your child – Apple Support (AU)

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. 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. See Winston Churchill's response in the below discussion. If possible, 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.      

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

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

Sign out of the Apple ID on one of the devices. If you and another person are sharing an Apple ID and you want to separate then one of you would have to sign out of the Apple ID and create a new one. If you want content from the other apple is that you used to use you could airdrop that content to your device with the new Apple ID or go to iCloud.com on your device and sign in with your old Apple ID and straight download that content onto your device your using with your new Apple ID.