Manage notifications from Messages on Mac
You can choose to get notifications for every new message, each time your name is mentioned, or when you receive a message from an unknown person. You can also turn notifications off altogether.
Manage notifications per conversation
In the Messages app
on your Mac, select a conversation.Click the Details button
in the top-right corner, then select Hide Alerts to stop notifications; to get message notifications again, deselect Hide Alerts.
If you have a trackpad or a Magic Mouse, you can also swipe left with two fingers on the conversation in the sidebar, then click the Hide Alerts button 
.
Manage all notifications
In the Messages app
on your Mac, choose Messages > Preferences, then click General.Do any of the following:
Notify me about messages from unknown contacts: Select if you want to be notified when you receive a message from someone who doesn’t have a contact card in the Contacts app
(even if the conversation is muted).Notify me when my name is mentioned: Select if you want to be notified when your name is mentioned (even if the conversation is muted).
Play sound effects: Select to hear the default sound effect when either of the above events occur or you receive a new message.
Choose the default sound from the “Message received sound” pop-up menu.
You can set options in Notifications preferences to turn off all notifications for Messages, change how the notifications appear, and more. To pause notifications from Messages, turn on Do Not Disturb or another Focus.