Donuts or Doughnuts get their name in the year 1809 when Washington Irving's reference to the Doughnuts in his history of New York is cited as the first written recording of the term Doughnuts.
Washington Irving described then the "balls of sweetened dough, fried in hog's fat, and called them what we know them as today as either donuts or doughnuts depending on how you like to spell it.
I've always spelled doughnuts "donuts" but either way is correct.
Doughnuts or donuts are also called olykoeks in some places or Doughnut holes.
The traditional spelling has always been Doughnuts and still dominates even in the United States though a lot people including myself call them donuts.
Either way they are delicious and I love them and wish I had some donuts right now.