The shared inbox has 5 default statuses to assign to tickets. These are:
'New'
'Open'
'Waiting for customer'
'Escalated to third party'
'Closed'
You can add extra statuses that apply better to your way of working:
Navigate to Settings Shared inbox Custom statuses for tickets click the plus sign.
Give your new status a name.
Click on “Save”.
You will now see your new status appear in the drop-down list next to 'Status' when you edit a ticket.