Cellophane was a failed tablecloth. Its inventor wanted fabric that would not stain, and got a clear film instead.
Jacques Brandenberger was a Swiss chemist working for a French textile firm, Blanchisserie et Teinturerie de Thaon. Wikipedia says that in 1908 he was inspired by a tablecloth that had wine spilled on it. He wanted a cloth that would "repel liquids rather than absorb them." He sprayed a waterproof cellulose coating onto viscose cloth. The cloth turned too stiff, but once dry the coating peeled away as a clear, unbroken sheet. He turned to the sheet instead.
Perfecting it took years. Adding glycerin to soften the film was the key step. Wikipedia says he had a machine to produce it by 1912, the year it was patented.
He named it himself. Etymonline dates the trademark Cellophane to 1912 and credits the coinage to Brandenberger. The first half is easy: cellulose, the plant fiber it was made from. Etymonline says English took that word from French around 1840, and it goes back to Latin cellula, "little cell."
The second half has two explanations. Wikipedia calls the name a blend of cellulose and French diaphane, "transparent." Etymonline says it is "probably" cellulose plus -phane, a Greek-based ending meaning "having the appearance of." Both roads lead back to Greek: diaphane comes from phainein, "to show, to bring to light." Either way, the name means something like "see-through cellulose."
The film found its market in candy. Whitman's began wrapping its Sampler chocolates in cellophane in 1912. DuPont built the first American cellophane plant around 1924. A DuPont chemist, William Hale Charch, then developed a lacquer that made it moisture-proof, introduced in 1927. By 1938, Wikipedia says, cellophane brought DuPont a quarter of its profits.
Success cost the name its owner in some places. In the United States the word is now generic, often used for any clear plastic wrap. In the UK and many other countries, Cellophane is still a registered trademark, now owned by Futamura.