Can I customize the auto email for event registration?
Registering people manually like in your comment will utilize the "Events - Registration Confirmation and Receipt (off-line)" template.

If people self register online, it will use the "Events - Registration Confirmation and Receipt (on-line)" template.

For reference, the templates are listed and available to edit from this screen:


  Administer > Communications > Message Templates > "System Workflow
  Messages" tab