Answer:
Duct tape is credited to Vesta Stoudt, who suggested a waterproof fabric tape for sealing ammunition boxes in World War II; Johnson & Johnson’s Permacel division then produced the first duct tape for the military. Details:

• Origins and inventor
  • Vesta Stoudt, an Illinois factory worker, proposed using a waterproof cloth-backed tape to seal ammunition boxes to speed access in combat. She even wrote to President Franklin D. Roosevelt in 1943, which helped catalyze official support for the idea. This led to Johnson & Johnson’s Revolite/Permacel division producing the first duct tape for military use, commonly known for its waterproof, cloth-backed composition.

• Evolution of the name and usage
  • The tape was often called “duck tape” due to the fabric (cotton duck) and its waterproof nature, and it became known in service as “100-mile-per-hour tape” for its versatility. Over time, it came to be widely known as “duct tape” as it was used to seal air ducts and other joints.

If you’d like, I can pull brief primary-source-style excerpts from the patent and company histories or provide a concise timeline.