My son publishes on Kindle under a pen name (legally the Copyright Office calls that a "pseudonym"). Heck, you can even publish anonymously. However, when you register you have to identify the real name of the claimant, which might be the publisher and not the author, so the public knows who owns the copyright. There are simple ways attorneys use to dodge that, however. Dummy corporate shell assignees, etc.
No, formalities such as copyright symbol, your name and year are necessary for your book to be copyrighted. Under 17 USC 102 copyright subsists once your book is fixed in a tangible medium of expression, which in these times usually means when it is saved to a computer disk somewhere, often in the "cloud". The USA adhered to an international treaty called the Berne Convention (named after Berne, Switzerland) more than 20 years ago that did away with formalities such as copyright notice or registration to secure copyright protection. The US is actually the exception in even having a Copyright Office or an official government registration process.
FYI, my son saves his ebooks on Google Docs, sends them to his lawyer (me) as proof of date of authorship, and now uses several eBook publishers other than Kindle , although everyone wants their eBook, wherever first published, to be listed on Amazon if they are going to maximize sales. Obviously, if you publish through Kindle that gets your book on Amazon since they own Kindle. Kindle has really opened book-writing to the masses and has dramatically lowered the cost of obtaining books to read. Funny thing is that so many people now skip the free books at the public library so they can have that electronic copy on their iPhone or Android smartphone or pad or their Kindle Fire.
Much of the Kindle process is actually automated, as you would expect with such a computer savvy company as Amazon. When their automated review kicks out a book, either you get an automated rejection with an automated explanation or eyeballs check it and see why the automated process did not accept it.
Amazon actually is somewhat ambivalent on whether YOU infringe a non-Amazon copyright as they are smart enough to be protected by a "safe harbor" legally (they lobbied heavily to obtain it) called the DMCA 17 USC 512 and they require all their sellers, including Kindle authors, to indemnify them or get banned from Amazon. Today, that is REAL POWER, as no author can really afford to bypass the world's largest bookseller if that author is money motivated.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
I understood what you posted here, but there really is no problem identified.
Under US law, your copyright interest attaches automatically once you complete and affix your work of original authorship in some tangible expressive format. You should always include the copyright notice but it is not required to demonstrate your rights.
Regards to your pen name, you can call yourself whatever you want. I would only use your legal name on legal documents however.
It is not clear what Amazon is asking for here, but I assume they do what they can to ensure that content provided from authors is original so to mitigate third-party law suits.
You should probably consult a lawyer in private to discuss your objectives over in more detail. Most of us here, including myself, offer a free phone consult.
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If you wrote the book, you automatically have a copyright on the work. You can use the circle C. If you want to register your copyright that is relatively simple and in expensive.
You can register with a pen name.
Amazon is completely independent of the copyright laws. Better you set your IP up correctly and protect your rights than try to get listed and give you your rights as an author.
It depndes on what you want to accomplish. In general, you are free to put the copyright symbol, my name and year, for the book to be copyrighted and ready to be published. and use a pen name instead of my real name.
This is not a legal advice or solicitation, and does not create an attorney-client relationship. Consult an attorney.