If you wish to receive notifications when you have do not disturb on or outside your work or business hours, you can enable this setting so you still receive silent notifications. Click into settings from the left-hand menu. Choose "Notifications" under the "Your account" section. Leave "Send notification while I'm off" toggled on to continue to receive notifications.
Toggle this option off if you don't want to receive any silent notifications (call or text notifications) when you have Do Not Disturb on or outside your business hours.
Turning off "Include message preview" will update your settings so that incoming text message notifications only display "New Message" and incoming voicemail message notifications only display "New Voicemail".
Note: If you mute a specific number to not receive notifications as outlined above then you won't need to make any further updates to your notification settings.