If you are self-publishing, your name can appear as the publisher in the copyright line. Even then, it is best to file official copyright documents with the Library of Congress. But I suspect very few independent authors do. Technically, an author’s work is already copyrighted the moment one finishes the work.
Here are some good answers from the U.S. Copyright office, https://www.copyright.gov/help/faq/faq-general.html#mywork:

“When is my work protected?

Your work is under copyright protection the moment it is created and fixed in a tangible form that it is perceptible either directly or with the aid of a machine or device.

Do I have to register with your office to be protected?

No. In general, registration is voluntary. Copyright exists from the moment the work is created. You will have to register, however, if you wish to bring a lawsuit for infringement of a U.S. work. See Circular 1, Copyright Basics, section ‘Copyright Registration.’ “

Publishing is one of the most complicated businesses on the planet. So, be prepared to learn the ropes. Licensing and copyrights are tricky and are best handled by an experienced literary agent or an attorney.