Disable Discord dock badge
Solution 1:
Discord also doesn't show up for me in System Preferences -> Notifications, however there are two places where Discord notification settings are, both accessible from the app.
From the top ribbon, click Discord > Preferences and there's a Notifications menu. From there you can disable Desktop notifications.
Additionally, if you right click each channel you're in you can see the per-channel notification settings.
Finally, in order to actually clear the badge after I turned notifications off, I right clicked each channel and clicked "Mark as read".
Solution 2:
It usually means you have an unread message in a channel. You can disable it by going to your System Preferences -> Notifications -> Discord -> Uncheck the "Badge app icon".