If he flies on the same plane all week long, it can and will be tracked, no matter who owns the plane or whose name it’s in. Because all countries have open and publicly available flight information. Planes are tracked by their tail number, which doesn’t automatically change when the plane is sold (the tail number can change, but that record will be public, too)
So, now instead of owning a plane, he just goes to private charter companies all the time. As a result, he does fly on different planes through the week. But they’re all non-commercial jets with only him and people accompanying him flying.