The "do" in "doughnut" refers to the well-kneaded flour used to make cakes and breads, and the "nut" refers to the "nut" of a bolt/nut. A nut has a hole in the middle and is used to fasten a hexagonal screw.
A doughnut is a flour dough shaped like a nut with a hole in the middle, and is fried in oil. The reason for this shape is that a doughnut with a hole in the middle can be cooked more easily than a manju-like dough when it is cooked in oil.
This is probably the reason why the first cooks made it with a hole in the middle. Nowadays, however, there are many doughnuts that do not have holes in them.