So, you're contemplating writing under a pen name but worry that doing so may obscure your legal rights to your work, is that the issue? If so, you can relax. Using a pen name when publishing a book doesn't change your legal name, rights, or responsibilities. You can be born Robert Smith on your birth certificate and go through life calling yourself Bob Adams, but that doesn't change your legal name, and it doesn't shelter you from your responsibilities under the law. Even if you were to sign a contract under a pseudonym, the law recognizes that the legal YOU signed it, no matter what name you used on the agreement, and YOU are legally responsible for all eventualities.
There's a good reason for this, of course. Except for the permanent responsibility (and rights) assigned to you as your legally registered self (most often determined by the name on your birth certificate unless legally changed by court order), you could change identities every ten minutes simply by using a pen name or pseudonym. You could claim that, since you used a pen name on a contract, that YOU aren't legally responsible for whatever "Robert Smith" didn't sign but "Bob Adams" did.
Extending this law to publishing means that, while you can use any pen name you desire on a publishing contract as well as on a published work, you're still your old legal self. Now, as a tradition, publishers will withhold an author's real or legal name in lieu of his or her desire to use a pen name and guard the author's true identity rigorously. But, as you might imagine, mistakes happen; cats slip out of the bag. Sooner or later you should assume that your real identity will be made public. If that event could be devastating to you and your career, you'd better think twice about writing under a pen name at all. It's probably not worth the risk.
Applying that legal principle to registering your book with the U.S. Copyright Office means that, while you should use your real name as registrant simply because doing so will make your undisputed proof of ownership easier should that become necessary, you're the copyright holder no matter what name you put down as author. I believe, however, that there's a stipulation with the copyright office that says you're required to register under your legal name and that you attest that you have done so upon your signature. Regardless of what name is on the book's copyright page as owner, however, YOU retain legal ownership of your work.
By the way, writers don't always elect to use pen names in order to shield their real identities from the reading public, as is commonly assumed. Although that's often the case, writers may also choose to use a pen name that seems more likely to appeal to their reading audience than their real names, resulting in greater sales. A writer of western fiction might choose to publish under the name of Buck Thorn rather than Percival Poorhouse. A writer of steamy romance novels might prefer the by-line of Delilah Silk to that of Jane Doe. In both of these cases, the writer's use of a pen name is done purely for economic purposes and doesn't affect the work's legal ownership.
Got all that? Good. Now ...
Smoke if you've got 'em.
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D. J. Herda is author of the new series of writing advice, About Writing Right, available in eBook, paperback, and hardcover formats at Amazon and at fine booksellers everywhere. You can check out his weekly column, "The Author-Ethicist," at Substack.com.