Hold down the shift key when you paste the objects into the new diagram. This will keep all of the naming information on the objects.
Thanks Dave, it works.
(And if you are using Capital rather than VeSys 2.0)
It used to be that this operation was prevented if there were any shared objects in the selection. However, this limitation has now been lifted.
We create new objects in the target design regardless of whether the source selected objects were shared or not.