In Canada, the term operating as (abbreviated to o/a) is used. In the United Kingdom, Ireland and Australia (and some parts of the United States), the phrase trading as (abbreviated t/a) is used. In several U.S. states, such names are also referred to as trade styles, fictitious business names, or assumed business names.
The distinction between an actual and a "fictitious" name is important because businesses with "fictitious" names give no obvious indication of the entity that is legally responsible for their operation. Therefore, for consumer protection purposes, most jurisdictions require businesses operating with fictitious names to file a DBA statement. This also reduces the possibility of two local businesses operating under the same name. Note, though, that this is not a replacement for obtaining a trademark. A DBA filing carries no legal weight in instances where a trademark would be necessary.
DBA statements are often used in conjunction with a franchise. The franchisee will have a legal name, but conduct business under the franchise's brand name (which the public would recognize). Thus, a franchisee for Imo's Pizza (a local St. Louis pizza restaurant) might have the legal name of "The Sauce Company, Inc. D.B.A. Imo's Pizza".
Notably in California and also in other areas, filing a DBA statement also requires that a notice of the fictitious name be published in local newspapers for some set period of time to inform the public of the owner's intent to operate under an assumed name. The intention of the law is to protect the public from fraud, by compelling the business owner to record his/her name with the County Recorder, and making a further public record of it by publishing it in a newspaper.