What is the best way to put your information on a tree stand when putting in on public land? So that it is weather proof?

I use a black sharpie laundry marker and put my hunter ID on the ladder or sticks, as well as the stand. Mark surfaces that are better protected from weather if possible, then shoot some rattle can clear coat over it.

I stamped my numbers into the legs of my ladder stand that's permanent & waterproof.

https://www.harborfreight.com/36-piece-14-in-steel-letternumber-stamping-set-60671.html

I use a brass dog tag with all the info stamped on it and attach it to the leg about 4 ft up. I drill 2 holes and pop rivet the tag on. You can usually get tags made at any hunting dog supplier. h.h