itch.io

You can set your game to private so it won’t show that you’re playing it or that you own it.

For Steam: Right-click on the game → Properties → Privacy → Set to Private

(Don’t forget to click the little arrow to also check the game’s DLCs if you have any.)

Be careful: if your Discord is connected to your Steam account, it can still show that you’re playing it. Just turn it off in your Discord settings:

Settings → Activity Privacy → Turn off Share your activity status while you play.