The examples and perspective in this article deal primarily with the United States and do not represent a worldwide view of the subject. (February 2018) (Learn how and when to remove this template message)
A trade name, trading name, or business name is a pseudonym frequently used by companies to operate under a name different from their registered, legal name. The term for this type of alternative name is a "fictitious" business name. Registering the fictitious name with the relevant government body is often required.
In a number of countries, the phrase "trading as" (abbreviated to t/a) is used to designate a trade name. In the United States, the phrase "doing business as" (abbreviated to DBA, dba, d.b.a. or d/b/a) is used. In Canada, "operating as" (abbreviated to o/a) and "trading as" (abbreviated to T/A) are used although "doing business as" is also sometimes used. 
A company typically uses a trade name to conduct business using a simpler name rather than using their formal and often lengthier name. Trade names are also used when a preferred name cannot be registered, often because it may already be registered or is too similar to a name that is already registered.
Fictitious business names do not create separate legal entities. The distinction between a registered legal name and a fictitious business name, or trade name, is important because fictitious business names may not always identify the entity that is legally responsible. Legal agreements such as contracts are normally made using the registered legal name of the business; and the legal name must be used whenever a business sues or is being sued.
In English, trade names are generally treated as proper nouns.
Numbered companies will very often operate as something other than their legal name, which is unrecognizable to the public.
In Chile, a trade name is known as a nombre de fantasía ('fantasy' or 'fiction' name), and the legal name of business is called a razón social (social name).
In Brazil, a trade name is known as a nome fantasia ('fantasy' or 'fiction' name), and the legal name of business is called razão social (social name).
In Singapore, there is no filing requirement for a "trading as" name, however, there are requirements for disclosure of the underlying business or company's registered name and unique entity number.
In the United Kingdom, there is no filing requirement for a "trading as" name, however, there are requirements for disclosure of the owner's true name and some restrictions on the use of certain names.
In several U.S. states, DBAs are officially referred to using another term. Oregon uses Assumed Business Names; Washington calls DBAs trade names; other states refer to trade styles or fictitious business names.
For consumer protection purposes, many U.S. jurisdictions require businesses operating with fictitious names to file a DBA statement, though names including the first and last name of the owner may be accepted. This also reduces the possibility of two local businesses operating under the same name, although some jurisdictions do not provide exclusivity for a name, or may allow more than one party to register the same name. Note, though, that this is not a substitute for filing a trademark application. A DBA filing carries no legal weight in establishing trademark rights. In the U.S., trademark rights are acquired by use in commerce, but there can be substantial benefits to filing a trademark application. Sole proprietors are the most common users of DBAs. Sole proprietors are individual business owners who run their businesses themselves, and are typically newer to the small business game. Since most people in these circumstances use a business name other than their own name, it's often necessary for them to get DBAs.
Generally, a DBA must be registered with a local or state government, or both, depending on the jurisdiction. For example, California, Texas and Virginia require a DBA to be registered with each county (or independent city in the case of Virginia) where the owner does business. Maryland and Colorado have DBAs registered with a state agency. And Virginia requires corporations and LLCs to file a copy of their registration with the county or city to also be registered with the State Corporation Commission.
DBA statements are often used in conjunction with a franchise. The franchisee will have a legal name under which it may sue and be sued, but will conduct business under the franchiser's brand name (which the public would recognize). A typical real-world example can be found in a well-known pricing mistake case, Donovan v. RRL Corp., 26 Cal. 4th 261 (2001), where the named defendant, RRL Corporation, was a Lexus car dealership doing business as "Lexus of Westminster", but remaining a separate legal entity from Lexus, a Division of Toyota Motor Sales, U.S.A., Inc.
In California, 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 first file or register his fictitious business name with the county clerk, and then making a further public record of it by publishing it in a newspaper. Several other states - Illinois for one - require print notices as well.