How can I transfer data to my new IPhone with different AppleID?

Realize you are working against how things are designed with each person supposed to have an Apple ID from the start. Make sure that each family member has a unique Apple ID - Apple Support

First transfer everything, not doing the ID change yet:

Click on this link --> Transfer data from your previous iOS or iPadOS device to your new iPhone or iPad - Apple Support to learn how to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch. Select one of the three options: Quickstart, iCloud, or iTunes/Finder.

Click here to see how to 'Create a new Apple ID' = create an Apple Account. --> How to create a new Apple ID - Apple Support

Merging Apple accounts (IDs) or transferring data is not officially supported, nor can it be done easily or completely. Read the links below for things you may need to do to transfer as much as is possible.

Apps and media bought with one ID are permanently associated with that ID. Look into using Family Sharing to continue to be able to use items purchased with one Apple ID with other Apple IDs.

- Family Sharing - What is Family Sharing? - Apple Support

- Set up Family Sharing - Set up Family Sharing - Apple Support

Share folders with iCloud Drive --> Share files and folders in iCloud Drive on iCloud.com - Apple Support

Read How to use Shared Albums in Photos on your iPhone, iPad, and Mac - Apple Support about about how to share photos.

If you have signed into the first ID on a device then fortunately when you sign out of that ID, do not erase the device, then sign in with a different ID, it asks you in most cases if you wish to merge the data from the two IDs on your device. Say yes and later delete individual items from the other ID that you do not want.

Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac --> Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac - Apple Support

If another Apple ID is signed in you may need to enter the password for that ID to sign out of that ID first.

Click on this link to learn how to 'Sign in with your Apple ID' --> Sign in with your Apple ID - Apple Support

Additional contributor posts:

- Apr. 2018 post by ASC helper Winston Churchill on transferring data from one Apple ID to another. Can I merge two iCloud accounts - Apple Community

- Feb. 2021 tips from Eric Root Apple ID - Apple Community