If you plan on using a fictitious name (also referred to as a DBA), you should check with your county clerk as to how to register a fictitious business name (or you can use one of the many DBA registration services online). The purpose of registering is so that the public can determine who owns a business. Most states only require sole proprietorships or partnerships to register if the fictitious business name does not include the names of the owners. If you're a sole proprietor (single business owner) and you are using a fictitious business name, you shouldn't have a problem registering the copyright. (This circular explains the basics for registering film.) When you file, list your real name as the copyright claimant (the owner of the copyright).
What if a copyright examiner sees that the owner listed on the notice differs from the owner named in the application? Explain that you used a DBA (and furnish proof of registration, if necessary).
FYI - If you are using a pseudonym, review your options before filing.
PS You have copyright without filing registering; it's automatic.