Turn off notifications for a conversation
If you don’t want to get notifications each time there’s a new message in a conversation, you can turn on Do Not Disturb.
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). For more information, see Receive or stop notifications.
Select a conversation, then click Details in the top-right corner.
Select Do Not Disturb.
To get message notifications again, deselect Do Not Disturb.
If you have a trackpad or a Magic Mouse, you can also swipe right with two fingers on the conversation in the sidebar, then click the Do Not Disturb button .