Good question. If your book is published by a traditional publisher, your name as the author will appear on the cover and front matter. But the traditional publisher usually files the copyright at the Library of Congress on behalf of the author, and will show the publisher’s name, not yours, as licensee.
The publisher’s contract with you determines how long a company has the right to publish the work under the author’s copyright. Often the terms are for the life of the copyright, which in most cases means the life of the author, plus 70 years.
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.