Zoom handles the email notifications to your class registrants. Yes, they do offer the ability to customize the notification emails with your branding. This feature requires an upgrade:
Here is what a basic unbranded email looks like from Zoom:
The From Name and Email if your client has any question can be customized in your automation.
Zoom classes created by our automations are password-protected, so the emails would also contain that info for your registrants to access your meetings. That helps to avoid unwelcome people "zoombombing" your meetings.