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.