What I mentioned is one way to show that info. It would require routing the DID to a ring group, set the desired info in the preferred "prefix" field and set the ring group to call whichever phones needed.
This allows the original CID information to be seen but also gives you an indicator of what number/department/etc was called.
Another way would be to edit the inbound route for each DID to reset caller_id_name or caller_id_number to be equal to ${destination_number}