I might be wrong, but here is how the system works in TC as I understand it.
Even when enhanced Mode S equipped, TC display your callsign on the radar using the code callsign data base, taking your callsign from the flight plan and using the A code(4096) assigned to the flight.
The Mode S details come from the FMS and show, selected flight level (displayed as an altitude below the transition level),ground speed,IAS and heading. The selected flight level is always shown, the other items are selectable.
We do not receive the aircraft callsign from the FMS.