If you own a fairly recognizable aircraft there really isn’t anything you can do. Making ADS-B data completely private would break its purpose (both ATC and other planes need to be able to pick it up). FAA has some programs to let you rotate your ICAO address but you can only request a new one every 20 days (and it can be a pain to change depending on your avionics) so it’s easy to link it back up.

At the end of the day, all of these systems are defeated by people with eyes at airports. We can’t repaint tail numbers every flight…

The more private (but still flawed) solution if you care more about privacy than having your own jet is to fly charter (NetJets, etc).