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.

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