If the identity of a backup disk has changed on Mac
For security, Time Machine won’t do a backup if it detects that the identity of your backup disk has changed. This can happen for several reasons:
You erased or reformatted your backup disk or partition.
You deleted the disk image for your backup disk.
You connected another disk to your Mac with the same name as your backup disk.
Someone is trying to steal your information by tricking your Mac into backing up to an unauthorised disk.
If you connect another disk to your Mac, give it a different name from your backup disk. Then make sure your backup disk is correctly identified. On your Mac, choose Apple menu > System Preferences, click Time Machine, then reselect your backup disk.