Perhaps I have found the solution to the puzzle.
When I am preparing to fly my aircraft in 2D, I load the data in the link16 page of the DTC via L16 plan. Before I press this button, the link16 data from the last flight are in the DTC.
If as in the case described I change as a member to another flight, I would like to have the flight plan data of this flight on the DTC.
I stay in my aircraft, select the other flight in the missions display without to click an AC and press save in the DTC.
I then have the flight plan from the other flight in my DTC and my STN is displayed. Perhaps something is running differently in the background, so that other STNs are loaded into the DTC?
I have just tested again:
2D DTC called up, pressed CLEAR, there were no STNs in the DTC display. In the aircraft I opened the Flight data page in the MPCD, there was no data of the buddies in it, as in the 2D DTC. In the OWN DATA page, however, there was the STN intended for me, although 00000 was saved in the DTC.