If you want to change the caller ID for numbers in your iPhone you can tap the Phone icon, then tap Recent to see the numbers you’ve called and ones that have called you. Find the number of the caller ID that you want to change and tap the arrow on the right and add as a contact. Fill out the contact information and tap Done. At that point you will be able to set the caller ID.
If you want to change how your calls come up on someone else’s caller ID, then finding an app that allows you to change that will help. One free App, called Voxox is an easy one that will allow you to get a free phone number that will set the caller ID and you can change it whenever you want. To do this, just launch the Voxox app, choose Settings and scroll to the called ID and click on the number. Then, just delete the number and add whatever you like and click Done