Final answer:
A pseudonym that companies use to operate under a different name from their legal one is known as a 'doing business as' (DBA) name or trade name. This differs from a trademark, which is legally registered as representing a company or product.
Step-by-step explanation:
A pseudonym used by companies to operate under a name different from their registered legal name is commonly referred to as a 'doing business as' (DBA) name or trade name. This is different from a trademark, which is a symbol, word, or words legally registered or established by use as representing a company or product. Companies often use a DBA when they want to enter a new market or project a certain brand identity without creating a new legal entity. For instance, a company's legal name might be 'XYZ Corporation', but it does business in the consumer market as 'Honeycrisp Apples'. Trademarks, on the other hand, protect the brand identity on specific goods or services, like the distinct shape of a bottle or a unique logo that distinguishes a product in the marketplace.