A sole proprietor, or in theory another business entity (such as a corporation, partnership, or LLC) can be "doing business as" some trade-name. I, for example, sometimes do "business" as "AK Lawyer, the sarcastic". (as in my previous post).
But my point was that a question for "specific forms" cannot be answered without knowing the specific jurisdiction. While the federal government does regulate an ever-increasing portion of our society, the regulation of the circumstances under which one may use a fictitous name for business purposes is still under state (or perhaps local) perview. Also, you might want to reserve a fictitious name so as to prevent others from using the same name. There are optional procedures for doing that in many places. You should also as a precaution check to see that someone else has not beat you to it, and has already reserved the name.
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