Yep, you have to click on a user's profile and then click on the blue button with a vertical ellipsis (...) in it, to the right of their profile picture. In this popup menu, choose "Start new chat with [name]".
If you're unable to find your mentor's name, try asking her in one of your lessons or email her if you have her email address
EDIT: An SCF administrator might be able to find your mentor's profile for you as well. @Mike-Cleveland