Typically, a company will have both a legal name and a trade name. Their legal name is the one that appears on government and legal forms, like their Articles of Incorporation—documents a company must file with the state department to legally form a corporation.
Businesses will likely use their trade names for the purposes of sales or advertising. Think of them as almost a nickname for the company.
For instance, Disney Consumer Products and Interactive Media is branded under the trade name The Disney Store, which is pithier (and less of a mouthful).
Corporations also use trade names to differentiate their brands, especially if they make a variety of products for different demographics.
For instance, Banana Republic, Old Navy, Athleta, and Intermix are all different stores with different inventory, but all of them are registered Gap Inc. brands.