If you don't see the "My Request" section in the sidebar of the Engage Client, as below it means you haven't been set in the staff browser to be able to accept requests.
To resolve this, you, or someone with access to the Management Console will need to edit your account.
They will need to go to the "Staff" page under "Advanced" in the Management Console
Once on the staff page, locate your self (or the user you're modifying in the list) and click the pencil icon to edit them.
It will take you to the editor page where you can tick the "Can Accept Message" box.
You'll then be prompted to enter a display name, do this and then click save
The user will then just need to log out and back in again to see the "My Requests" section and be able to have request assigned to them.