There are two ways to turn off chat notifications in Teams. You can either mute the chat, or turn off notifications.
To mute a current chat
1. Either right-click on the chat or click on the ellipses, and select Mute.
To turn off notifications
1. In Microsoft Teams, click on your profile picture.
2. Next, select "Settings."
3. When the "Settings" window pops-up, click on "Notifications."
4. Under "Chat" click on the "Edit" button.
5. Depending on which one you choose or for all of them, select either "Only show in feed" or "Off."