How to disable location display icon (own-ship display)
.... on my location when I type the center icon on the Avare screen, but I don't want the location display icon (referred to as own-ship display by the FAA) ...

Avare has as remedy for this by providing a transparent icon so your own ship is not displayed. See https://apps4av.com/avare-overview/c...ernal-gpsadsb/
There are also a number of YouTube tutorials for using a Avare And I seem to recall the issue being resolved in at least one of them.