There currently is no easy way to search for a registrant name in the Registration Records screen. If you have an event with 200 registrants for instance, it's an absolute pain to search for a specific registrant to see his payment status for example.
Please add a search box similar to the one in the User Manager screen of Community Builder.
I agree this would be a really useful tool in fact I would like to see a filter search box on the all records page too similar to the one used in Acajoom so you can search all events.