You can label conversations in a Collaborative Inbox to assign them to a particular category. 

To add a label to all conversation:

Expand the Labels heading on the left-hand side of the screen to show all labels. Click on a label to show only the conversations that have been assigned to that label.

You can remove a label from a conversation by clicking on the X to the right of the label along the top of the message. name. 

Click on the Conversations link on the right-hand side of the screen to return to viewing all conversations in the collaborative inbox.