You also deserve credit for not calling it, like some people do, Duck Tape. (Quack,quack.)
Duck Tape is an actual brand.
I saw some in the hardware store a few years ago, and it said Duck Tape. I assumed that was just a knockoff 'brand' name (because it was some pretty crappy tape).
I have called it Duct Tape all my life.
HOWEVER, the truth is that there is a specific 'type' called DUCT TAPE and it is designed just for air ducts.
However, the ORIGINAL tape was invented for use by the Military, and it was called DUCK TAPE. What you can buy at the hardware store NOW is (imho) neither DUCT TAPE nor DUCK TAPE. However, that is not the issue.
Bottom line: DUCK TAPE is the original and proper name for that particular type of tape.
I wouldn't have believed it if I hadn't researched it.
Actually, the original name was Duck Tape when it was invented early in the 20th century. Later it became common to use it with heating ducts and it became more common to call it “duct tape”. Both versions survive. I always thought it was duct tape, and that duck was a mistake. Read an article not long ago setting out the history.