If you have to change your email address associated with your Apple account then you will have a new Apple ID because your email address has now changed. Now when you see iCloud account details in your other Apple devices (iPhone, iPad), you will see the old Apple ID being displayed there. You have changed the Apple ID but because you have not changed it for iCloud in your Apple devices, all backups will be associated with the old Apple ID that is stored in iCloud account in your devices. Here is how to change Apple ID for iCloud in your device, when you have changed your Apple ID.
Simple way to change your iCloud ID on your Apple device is to go to Settings > iCloud in your device, tap Delete Account (it will ask old ID and password), sign back in with the new ID. This deletes the iCloud account and your iCloud data from your device, but not from iCloud. If you sign back in on your device, with old iCloud account, your iCloud data will reappear on your device.
Another way is to go to MY Apple ID online and change apple id to the old one, save it. Go back to device and delete icloud account, go back to online Apple ID and change ID back and save it. Go back to device and go to icloud and sign in with new id and password.
If you still have access to your old email address, do the following:
Proceed to My Apple ID
Click ‘Manage my Apple ID’.
Sign in with your iCloud ID.
Tap edit next to the primary email account.
Tap Edit, change it back to your old email account and verify it.
Then edit the name of the account to change it back to your old email address.
You should then be able to turn off Find My iPhone with your password.
Then go to Settings > iCloud.
Tap ‘Delete Account’ and choose ‘Delete from My iDevice’ when prompted (your iCloud data will still be in iCloud).
Go back and change your primary email address and iCloud ID back to the way it was.
You will then be able to go to Settings > iCloud from your device and sign in with your current ID and password to reconnect to your iCloud account.