Yes, you can. If you running a business you can register the d.b.a with your state.
As for registration you can do it with pseudonym or even anonymous, as you wish.
The important thing to remember is that it is a pen name, not your name and you should not sign any contracts or present yourself as your pen name.
USPTO Registered Patent Attorney, Master of Intellectual Property law, MBA I am neither your attorney, nor my answers or comments in AVVO.com create an attorney-client relationship with you. You may accept or disregard my free advice in AVVO.com at your own risk. I am a Patent Attorney, admitted to the USPTO and to the Florida Bar.
You can use a dba as long as you are not misleading or trying to impersonate someone else.
Please note that I am answering this question as a service through Avvo but not as your attorney and no attorney-client relationship is established by this posting. An attorney-client relationship can only be established through signing a Fee Agreement and paying the necessary advanced fees.