When registering a stage name with the US copyright office do you register as a goods or a service. i.e. Performing and recording under pseudonyms

First, it sounds as if you are talking about registering a trademark, not a copyright. You register a trademark with the United States Patent & Trademark Office. You may want to register as both goods AND services. You may register for audio and video recordings that are offered under that stage name as goods. You may also want to register for entertainment services.