iPhone - go to system and notifications and under notification style, choose the notification options you want for the Discourse hub app. as far as I know that is how I do it on mine (I just changed sounds and toggled them off that way now to test it).
If you are using browser, then it should be the same way, but pick the browser instead of the hub app. And of course check your tracking and notification settings in your Discourse user preferences for those specific forums to make sure they are turned on and configured to how you want.