To add a patient to Engage, you'll need the patient's email address to invite them in. Click the "+" icon at the top right of the team name header. Then select "Invite Patient". Enter the patient's email address and make sure you get a positive confirmation that the invitation has been sent.
Once the patient has accepted the invitation and registered for Engage, their name will appear in the Browse Patients list, and on the left sidebar (until you choose to close or leave the room).