Dope, I thought that someone else had this pain in the past, but I had to admit did not searched the TJC posts properly.
Anyway I think it’s time for patching!
Looked around the voicecall-ui-jolla and found out the following:
calling/IncomingCallView.qml has a person member which got filled from the callerDetails of the telephony object which lives in the VoiceCallManager.qml.
In the VoiceCallManager I have not been able to trace where the callerDetails got filled.
It is even possible that all contact details are present there, however I do not know how could I run it to see the command line output (a console.log(callerDetails) would reveal if the company details are present or not).