Btw, let me add… after about 5 mos, neutering often has NO effect on marking behavior.
You should also treat ANY new dog, puppy or adult, as a puppy. Which means you either have them leashed to you, crated, or actively watching every single move. It is far easier to stop marking from starting (or any bad behavior) than correcting it once establish. You also need to go back to that when marking or other unwanted behaviors start. Sure, it's a pain in the butt, but easier than letting it become a habit then try to retrain.