If your registrants have account on your site, you should create a menu item and select Registration History menu option of Events Booking so that your registrants can login, access to that menu item, see list of events which they registered, download invoices....
Go to Events Booking -> Configuration, look at Themes tab, Registration History section, you can change some settings to:
If you still want to customize it more, you will need to customize code in the file components/com_eventbooking/themes/default/history/default.php . Remember that once the change is done, you should move the modified file to PATH_TO_TEMPLATE/html/com_eventbooking/history folder so that the change won't be lost when you update to future releases of the extension.