Log Off: Where the Name Came From

We sell logs, or things made from them. "Log off" was sitting right there, and once you notice a pun like that you cannot unnotice it. It ended up on a tee and a trucker hat because some jokes deserve to be worn, not just said once and forgotten.
It also happens to describe the actual use case. Nobody buys a stump table or a whiskey smoking kit because they need more screen time. They buy it because they are trying, in some small furniture-adjacent way, to log off.
We are not going to explain the joke any further than this. If you get it, you get it. If you don't, the hat still looks good.