It’s possible to change the UUID on the VDI file using the command:

 VBoxManage internalcommands sethduuid <file.vdi>

It looks this command assigns a new “random” UUID to the file. No much documentation on it, though.

Note: The solution by ABC is a workaround that works only if you want to remove the already existing disk with the same UUID. If that one is bad, then yeah, remove it and problem solved. However, that was not my case since I needed to use both disks.

Source: VirtualBox Cannot register the hard disk already exists – Stack Overflow