Ahhhh, this old chestnut.
In my humble opinion the PIN should be called the deep branch of the radial nerve once it leaves the main trunk of the radial nerve. This is the division of the radial nerve into superficial and deep branches. It should only be called the PIN when it emerges from between the supinator muscle bellies and sits on the posterior aspect of the interosseous membrane. I don’t think it should be called the PIN as it enters the space between the supinator heads at the arcade of Frohse. I think at this level it should be called the deep branch of the radial nerve. But like you say, good luck changing what everyone says these days.
Let’s start a campaign !
Steve.