"The first recorded use of the term Buckeye to refer to a resident of the area was in 1788, some 15 years before Ohio became a state. Col. Ebenezer Sproat, a 6’4" man of large girth and swashbuckling mannerisms, led the legal delegation at the first court session of the Northwest Territory in Marietta. The Indians in attendance greeted him with shouts of "Hetuck, Hetuck" (the Indian word for buckeye), it is said because they were impressed by his stature and manner. He proudly carried the Buckeye nickname for the rest of his life and it gradually spread to his companions and to other local settlers. By the 1830s, writers were commonly referring to locals as “Buckeyes.”
This was taken from this website .
http://ohiostatebuckeyes.collegesports.com/genrel/buckeye.html