If you like to use a cloned volume with a volume group on it, then normally you will have a problem with the VG UUID and the VG Name. The good answer there is a nice solution for the problem and you can import and rename duplicated volume groups.

To rename and generate a new UUID for the volume group on the volume use the program vgimportclone.

After the successfully rename of the volume group activate it.

Now you can use the renamed volume group old normally as other volume groups.