The following is the text of U.S. Copyright Office's publication on filing a pseudonymous work, also linked below:
A pseudonym or pen name may be used by an author of a copyrighted work. A work is pseudonymous if the author is identified on copies or phonorecords of that work by a fictitious name. Nicknames or other diminutive forms of one’s legal name are not considered fictitious. As is the case with other names, the pseudonym itself is not protected by copyright.
If you are writing under a pseudonym but wish to be identified by your legal name in the records of the Copyright Office, you should give your legal name and your pseudonym when filling out your application. Check the box labeled “Pseudonymous” if the author is identified on copies of the work only under a fictitious name and if the work is not made for hire. Give the pseudonym on the associated line.
If you are writing under a pseudonym but do not wish to have your identity revealed in the records of the Copyright Office, you should give your pseudonym and identify it as such. You may leave blank the space for the name of the author. If the author’s name is given, it will be made part of the online public records produced by the Copyright Office and will be accessible via the Internet. This information cannot be removed later from those public records. You must, however, identify the citizenship or domicile of the author.
In no case should you omit the name of the copyright claimant. You may use a pseudonym in completing the claimant space, but you should also be aware that if a copyright is held under a fictitious name, business dealings involving that property may raise questions of ownership of the copyright property. You should consult an attorney for legal advice on these matters.
If the author is identified in the records of the Copyright Office, the term of the copyright is the author’s life plus 70 years. If the author is not identified in the records of the Copyright Office, the term of copyright is 95 years from publication of the work or 120 years from its creation, whichever term expires first. If the author’s identity is later revealed in the records of the Copyright Office, the copyright term then becomes the author’s life plus 70 years.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.