Apple has no formal account merging or transferring process. The things below will help you in doing ongoing or one-time transfer of as much as possible from one account to the other, but some things can never be transferred (namely purchases), only shared.
You can use various iCloud sharing features for some ongoing data sharing.
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 how to share photos.
Sharing music playlists —> How to share an Apple Music playlist on your iPhone or iPad - Apple Support
Apps and media bought with one Apple account are permanently associated with that account. Look into using Family Sharing to continue to be able to use items purchased with one Apple account with other Apple accounts, and for some data sharing features.
- Family Sharing - What is Family Sharing? - Apple Support
- Set up Family Sharing - Set up Family Sharing - Apple Support
If that is all you are interested in merging, you probably don't need to do anything more than set up Family Sharing.
The next section may sound tricky but it lets you merge some things on a device where you have already signed in with an old account but want to use a new account and incorporate data that is already on the device from the old account. Incidentally, the data will then propagate to other devices using iCloud with that new account. (I haven't tried this with a computer but it may also work with a computer account signed into an old account.)
If you have signed into the first Apple account on a device then fortunately when you sign out of that account it asks you if you wish to retain the data from the old account on your device (toggle the ones you want to on). If you keep data on the device then when you sign in with the other account it will merge this data with the account signing into the device. You can later delete individual items from the old account that you do not want. Similar information can be found in this post: I have 2 apple IDs i want to merge them h… - Apple Community , and a step-by-step in this User Tip: How to “unshare” an Apple ID - Apple Community . Note that only content physically present on the device such as contacts, photos and videos will be retained. Meta data such as a game play scores that are tied to a specific account or are only on a vendor's Apple Account-specific database remotely will not be retained. Also turn off storage optimization before doing this. With Optimize Storage, smaller, space-saving photos and videos are kept on your device while all of your original, full-resolution versions are stored in iCloud. Make sure photo optimization is turned off so the full quality versions from the old account are actually on the device before merging the content into your new account. Manage your photo and video storage - Apple Support You can turn optimization back on again once you are fully using your new account on the device.
Even though apps may remain on a device and may work for a while, you will not be able to update them or redownload them unless you buy them again with this account or download them with this account using Family Sharing.
Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac --> Sign out of iCloud on your devices - Apple Support
If this involves a device changing ownership, the person should also change the ID set in Find My. Turn off Find My on your devices and items - Apple Support
If another Apple account is signed in you may need to enter the password for that account to sign out of that account first.
Click on this link to learn how to 'Sign in with your Apple ID' --> https://support.apple.com/HT204053
