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.To search for contacts and content in conversations, click in the Search field in the top-left corner and enter what you’re looking for. Or choose from the suggested contacts, links, photos and more.
If you’re restricted to sending and receiving messages with only certain people, an hourglass icon
Click the Details button
in the top-right corner, then select Hide Alerts to stop notifications; to get message notifications again, de-select 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.Select or de-select any of the following:
Notify me about messages from unknown contacts: If you select this, you are 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: If you select this, you are notified when your name is mentioned (even if the conversation is muted).
Play sound effects: If you select this, the default sound effect plays 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.
To turn off notifications for all messages, change your Notification preferences. You can also change the type of notifications you receive for messages (for example, playing a sound or showing a badge on the Messages icon in the Dock). See Receive, pause, or stop notifications.