The verb to duck came first. The birds are called ducks because they often duck underwater.
Both meanings of the word duck trace back to Old English, over a thousand years ago.
The verb to duck (“to lower the head or body suddenly” per Merriam-Webster) comes from the Old English ducan (/duːkɑn/) meaning both to duck and to dive.
The noun duck (e.g. Donald, Daffy) comes from Old English duce (/duːkɛ/). Duce is derived from the verb ducan and more literally means ducker or one who ducks.
Interestingly, the first recorded use of the word duck (not ducan or duce) came from before the 12th century, first referring to the noun. The first recorded use of duck as a verb wasn’t until the 14th century, most likely because there was more reason to write about ducks (as both game and farm animals) than ducking.
Both definitions of the word duck have been around for since Old English developed into Modern English, but the verb came first (originally as ducan). The animals were first called ducks because of their tendency to duck under the water.
The verb “duck,” meaning to dip, plunge, or dive, is what gave the waterfowl its name. The bird is called a “duck” because it “ducks” or dives below the water’s surface.