You cannot merge Apple ID's.
You can log out of the Apple ID on one device and log in with the one you want to keep.
There's 4 places that are signed in with your Apple ID.
Settings ➜ Account (top of Settings), (scroll to the bottom for the Sign out option)
Settings ➜ Account ➜ Media & Purchases
Settings ➜ Messages ➜ Send & Receive ➜ Apple ID
Settings ➜ FaceTime ➜ Apple ID.
Do note:
Purchases such as Movies, TV Shows and Apps are tied to the Apple ID that made them, and cannot be transferred to another Apple ID. In the case of Apps, they will always require the password for the Apple ID that was used to download them to update.
Content such as contacts, notes, files and photos stored in iCloud on account will need to be manually downloaded and transferred onto the other account. There is no automatic process for this.
Once you are sure you no longer need the other account, you can request its deletion. click here ➜ How to delete your Apple ID account - Apple Support
Make sure you sign out of every device using the Apple ID you want deleted before requesting deletion as it cannot be done after, and the devices will be unusable if not signed out once the Apple ID no longer exists.