To change your display name while participating in a 'live' session on a computer, click on the Participant option at the bottom of the screen as shown:
Next, click on the three little dots next to your display name as shown:
Next, click on Rename and then save it. You now have a new display name for this session.
If you are logged in the live session on a mobile device such as an iPad, the Participant option is in the upper right corner of the screen. Click on your name and the Rename option will appear. On an iPhone, the Participant option is at the bottom of the screen. Click on your name and the Rename option will appear.