For most of the 20th century, Nabisco was not the company's legal name. It was a nickname that the public and the marketing team used long before the lawyers caught up.
The company itself was born on 19 June 1898 in Chicago. Three bakery groups merged to form the National Biscuit Company. They were led by William H. Moore, Adolphus Green and John G. Zeller. One company history says the new firm began with 114 bakeries and $55 million in capital.
Green, a Chicago lawyer, became its guiding force. He picked a single cracker to put the company's name on the map and sold it in a small cardboard box lined with waxed paper. The N. W. Ayer advertising agency suggested the brand name Uneeda Biscuit. By 1900 the company was selling more than 100 million packages a year.
Nabisco grew out of that same branding push. The name takes the first syllables of each word: National Biscuit Company. One company history says it first appeared as a possible name for the Uneeda cracker. Wikipedia dates its first use as a product name to a cracker brand in 1901.
For decades the official trademark was simply "N.B.C." That became a problem once the National Broadcasting Company took to the airwaves with the same initials. In 1941 the company switched its trademark to "Nabisco," partly to end the confusion.
Even then, the corporate name stayed National Biscuit Company. It did not officially become Nabisco until 1971. By then the nickname had been printed on boxes of crackers and cookies for generations.
The short name outlived several owners. A 1981 merger with Standard Brands created Nabisco Brands. In 1985 R.J. Reynolds bought it, forming RJR Nabisco. Philip Morris acquired it in 2000 and folded it into Kraft. Since 2012 Nabisco has been part of Mondelēz International, where it survives as a brand.
So the name on a box of Oreos is an abbreviation that started as shorthand and ended up outlasting the company it abbreviated.