I do not have detailed knowledge of the working of GSMR, at the start of a journey, and when opening up the cab, the Driver registers with the signalling system with detail of the headcode of the movement and the number of the signal if berthed at a signal, a wildcard number if there isn't a suitable signal. At the end of the journey, the Driver deregisters the headcode, the system is geographical in operation, but not foolproof, just one example phoning a Signaller while standing at Peckham, a Victoria panel area, Romford box responded.
The train describer system (in panel boxes this is usually a standalone system, in vdu control centres it is now just one part of the control system software) is what moves the 4 character train descriptions around the panel as the trains move. The descriptions are usually entered manually by the signaller at the start of the journey, but in those boxes with Automatic Code Insertion the train describer may do it automatically. As far as I am aware, the train describer does not rely on the GSMR for its operation, the train describer will keep happily working without GSMR (and many TDs were installed before GSMR even existed).
The GSMR system knows the unit identity of the train it is installed in, but that is not how signallers usually contact the train. They know trains by their train description as displayed on the panel by the train describer, or its position at a certain signal, they won't readily know what unit that train is being worked by, or it's GSMR "phone number" At the start of a journey, the driver therefore has to register the train description for that service with the GSMR system. The GSMR system can then correlate the train's "phone number" with the unit number, train description and location (the train describer berth that description is currently being displayed in, usually based on the signal number). As the train moves along it's journey, the train describer will keep the GSMR system updated with the location of it's train description. So if at any point, if the signaller wants to contact train 1A23 or the train standing at signal S456, the GSMR will know which GSMR radio unit to call.
Likewise if the driver asks to call the signaller, the GSMR should know where that train is in railway terms, i.e. which signal berth it's description is stored in, and therefore which signaller is responsible for it. I suspect that the reason that you may occasionally get the wrong signaller could be because say both Victoria and Romford have trains with the same train description on their patch.