Each of your teammates on your app controls their own notifications via their personal account settings. To change your notification settings, just open your 'Your account' in your hover menu, then select 'Notifications .'
Note: You'll need the Inbox product to get the full range of notification options. If you don’t have Inbox, you can only choose to be notified of all all new conversations via browser notifications (or you can choose to get no notifications).
Assigning someone else
You can assign one person to receive all new messages. That person can then re-assign the message to someone else on the team. You can also assign all messages to a particular team based on assignment rules.