I registered my penname. I plan to get the book copyrighted, and that's a step that has to be taken. LALAALALALALALALALALALALA, LOL!
In most states in the US, one has to register with the Secretary of State for one's state of residence, any name under which one receives money, payments, royalties. That includes pen names for authors. Usually there's a web page on one's Secretary of State website, where one can go and, for any individual or partnership, create a 'profile' and then under that 'profile', specify any names under which that individual or partnership, does business. The idea is that everyone needs to report all the income they get so they get taxed on all their income. In the past, people have used pen names to try to weasel out of paying taxes.
OK. Sometimes people are talking about trademark registration. When it comes to DBAs and the like, you may or may not need one for a pen name. As you said, if you're receiving payments under that name, you have to take the appropriate steps to set things up properly. In some cases, authors publish under a pen name but conduct all business under their normal name, in which case filings with the Secretary of State shouldn't be necessary.
My pen name is a registered trade mark. A pen name need only be "registered" in the USA if a person is doing business *AS* that name (not "under" that name). In other words, the writer should set up a tax-payer ID under the name of her business, under which she must send quarterly reports to the Internal Revenue "Service." My pen name and my trademark is DESERTPHILE. My business is DESERTPHILE PUBLISHING. The former was filed with the United States Department of Patent and Trademark; the latter was filed with the IRS.