Also called a trade name, ficticious name, or "doing business as" (DBA), an assumed name is a name you are using other than the legal name of the business. If you are a sole proprietorship, your legal name is your own name; if your business is a partnership, LLC or S-Corporation, the legal name under which the business was registered.
Most states required individuals or businesses operating under an assumed name to register the name. This allows someone trying to find a company to go to the state records and find the location and owners of the company either by the legal name or the assumed name. States generally prohibit more than one business using the same name. Typically it's Department of Corporations, the Secretary of State or a similar state agency that handles registering an assumed name. The Small Business Administration's search tool can direct you to the appropriate agency for your state.
Most often, assumed names are used by individuals operating as sole proprietorships who want to have a business name other than their own personal name. Assumed names are also used by partnerships or LLC's when a different name would be better for marketing or positioning purposes (for example, a DBA of "Sally's Soaps" might be better than "Smith, Jones, White and Green, Partnership"). See Choosing a Business Name for tips on how to pick a good business name.
For the purposes of labeling products for sale to consumers, the regulations require the "business name and address" be included on the label. The business name used should be the name under which the business is legally operating - either the legal name or a registered assumed name.
Keep in mind that registering an assumed name in one state does not protect you if someone in another different state wants to use the same name. Protection of your name across state lines must be done by trademarking the name, which protects it throughout the United States.