Entry in progress—B.P.
 
Wikipedia: Aesculus glabra
The tree species Aesculus glabra is commonly known as Ohio buckeye, American buckeye, or fetid buckeye. Glabra is one of 13–19 species of Aesculus also called horse chestnuts.
 
It is native primarily to the Midwestern and lower Great Plains regions of the United States, extending southeast into the Nashville Basin. It is also found locally in the extreme southwest of Ontario, on Walpole Island in Lake St. Clair, and in isolated but large populations in the South (Adams County, Mississippi). It is a medium-sized deciduous tree growing to 15 to 25 metres (49 to 82 ft) tall.
     
The Ohio State University
Origins of the Buckeye Name
The use of the term Buckeyes to refer to Ohio State University sports teams derives from the even wider use of the term to refer to all residents of the state of Ohio.
 
The university’s Athletic Council officially adopted the term in 1950, but it had been in common use for many years before—certainly it was firmly established by 1920, and most records indicate that it had probably been used with some frequency to refer to Ohio State and its athletic teams since before the turn of the century.
 
As with many such terms that seem to have evolved rather than been decreed, the history of “buckeye” is a bit fuzzy. The buckeye (Aesculus glabra) is a tree, native to Ohio and particularly prevalent in the Ohio River Valley, whose shiny dark brown nuts with lighter tan patches resemble the eye of a deer.
 
Wikipedia: Brutus Buckeye
Brutus Buckeye is the athletics mascot of Ohio State University. Brutus is a student dressed in Buckeye colors with a headpiece resembling an Ohio Buckeye nut. Brutus made his debut in 1965, with periodic updates to design and wardrobe occurring in the years since. As a member of the spirit squad, Brutus Buckeye travels to many events around the university and often makes appearances around Columbus.
   
Google Books
A Ramble of Six Thousand Miles Through the United States of America
By Simon Ansley Ferrall
London: Published by Effingham Wilson
1832
Pg. 68:
The corn was heaped up into a sort of hillock close by the granary, on which the young “Ohiohians” and “buck-eyes” — the lasses of Ohio are called “buck-eyes”— seated themselves in pairs; while the old wives, and old farmers were posted around, doing little, but talking.
 
2 November 1832, Salem (MA) Gazette, pg. 3, col. 2:
FROLICS IN AMERICA. (...) The corn was heaped up into a sort of hillock close by the granary, on which the young “Ohiohians” and “buck-eyes”—the lasses of Ohio are called “buck-eyes”—seated themselves in pairs; while the old wives, and old farmers were posted around, doing little, but talking.
 
Google Books
22 February 1834, New-York (NY) American, “Review of the Week,” pg. 2, col. 1:
There was a long-haired “hooshier” from Indiana, a couple of smart-looking “suckers” from the southern part of Illinois, a keen-eyed leather-belted “badger” from the mines of Ouisconsin, and a sturdy yeomanlike fellow, whose white capote, Indian mockasons, and red sash proclaimed, while he boasted a three years residence, the genuine wolverine, or naturalized Michiganian. Could one refuse a drink with such a company? The spokesman was evidently a “red-horse” from Kentucky, and nothing was wanting but a “buckeye” from Ohio, to render the assemblage as complete as it was select.
 
19 August 1834, New York (NY) American, pg. 2, col. 2:
NAMES. A writer in the Illinois Pioneer says: that, the following nick-names have been adopted to distinguish the citizens of the following states:—
 
In Kentucky they’re call’d Corn-Crackers,
Ohio, ....................Buckeyes,
Indiana .................Hoosiers,
Illinois ..................Suckers,
Missouri, ...............Pukes,
Michigan, T. ..........Woolverines.
The Yankees are called Eels.
 
OCLC WorldCat record
Buckeye & Gallipolis journal.
Publisher: Gallipolis, Ohio : Wm. Cary Jones, 1834-
Edition/Format:   Newspaper : English
 
OCLC WorldCat record
The Buckeye.
Publisher: Chillicothe, Ohio : W.C. Jones & Co., -1834.
Edition/Format:   Newspaper : English
 
Google Books
Trip to the West and Texas
By Amos Andrew Parker
Concord, NH: Printed and Published by White & Fisher
1835
Pp. 86-87:
Those of Michigan are called wolverines; of Indiana, hooshers; of Illinois, suckers; of Ohio, buckeyes; of Kentucky, corn-crackers; of Missouri, pukes; &c.

OCLC WorldCat record
Proceedings of the Buckeye celebration in commemoration of the day on which General St. Clair named ‘Fort Hamilton’ : at Hamilton, Ohio, on the thirtieth day of September, 1835.
Publisher: [Hamilton, Ohio?] : [publisher not identified], [1835]
Edition/Format:   eBook : Document : English
 
OCLC WorldCat record
The Buckeye jumper : or, Borton’s first present to the public, comprising six score and sixteen remarks concerning the science of medical botany.
Author: Jacob Borton
Publisher: Lebanon [Ohio] : Printed at the Office of the Western Star, [1835]
Edition/Format:   Print book : English
 
21 September 1835, Alexandria (VA) Gazette, pg. 2, col. 4:
In Michigan a Woolverine, and in Ohio a Buckeye. (...)—N. Y. Star.
 
7 November 1835, Gloucester (MA) Telegraph, pg. 2, col. 5:
The Editor of the Louisville Journal, speaking of Mr. Van Buren, asks: “Is it not well understood that he aims to be thought a ‘Buckeye’ in Ohio, a ‘Wolverine’ in Michigan, a “Hooshier” in Indiana, a ‘Corncracker’ in Kentucky, a “Sucker’ in Illinois, and a ‘Puke’ in Missouri? We think he is well entitled to be called a puke in every State.
 
Google Books
April 1836, The Family Magazine (Cincinnati, OH) , pg. 265, col. 1:
A native of Ohio is called a “Buckeye;” of Michigan, ” Wolverine;” of Indiana, “Hoosier;” of Kentucky, “Com-cracker;” and of Missouri, “Pewk.”
 
30 July 1836, Chicago (IL) American, pg. 2, col. 5:
The ladies of Wisconsin have determined and decreed, that now and ever hereafter they will be known as “Hawk Eyes.” Look out for your “Chickens” neighbor “Wolverines.” The “Suckers,” “Hoozers” and “Buckeyes” must also be on the alert.
 
23 August 1836, American Traveller (Boston, MA), pg. 2, col. 3:
The ‘Gothamites,’ ‘Pukes,’ “Bay State boys,’ ‘Granite boys,’ ‘Green Mountain boys,’ ‘Chickens,’ ‘Buckeyes,’ ‘Wolverines,’ ‘Suckhers,’ ‘Hooziers,’ ‘&c. &c. &c.’ will hereafter be compelled to yield the palm to the ladies of Wisconsin, who now and henceforth are determined to be known as the Hawk Eyes.
 
Google Books
Recollections of Europe
Volumes 1
By James Fenimore Cooper
London: Richard Bentley
1837
Pg. 289:
Your Wolverines, and Suckers, and Buckeyes, and Hooziers would look amazed to hear an executive styled the White Fish of Michigan, or the Sturgeon of Wisconsin; and yet there is nothing more absurd in it, in the abstract, than the titles that were formerly given in Europe, some of which have descended to our times.
 
Google Books
The Clockmaker; or The Sayings and Doings of Samuel Slick, of Slickville
By Thomas Chandler Haliburton
London: Richard Bentley
1838
Pg. 289:
These last have all nicknames. There’s the hoosiers of Indiana, the suckers of Illinoy, the pukes of Missuri, the buckeys of Ohio, the red horses of Kentucky, the mud- heads of Tenessee, the wolverines of Michigan, the eels of New England, and the corn-crackers of Virginia.
 
Google Books
8 September 1838, New-York (NY) Mirror (New York, NY), pg. 86, col. 2:
These last have all nicknames. There’s the Hoosiers of Indiana, the Suckers of Illinoy, the Pukes of Missouri, the Buckeyes of Ohio, the Red Horses of Kentucky, the Mud-heads of Tennessee, the Wolverines of Michigan, the Eels of New-England and the Corn-crackers of Virginia.
 
Google Books
The Attaché:
Or Sam Slick in England
By Thomas Chandler Haliburton
Paris: Baudry’s European Library
1843
Pg. 130:
Why, as I am a livin’ sinner that’s the Hoosier of Indiana, or the Sucker of Illinois, or the Puke of Missouri, or the Bucky of Ohio, or the Red Horse of Kentucky, or the Mudhead of Tennesee, or the Wolverine of Michigan, or the Eel of New England, or the Corn Cracker of Virginia?
 
OCLC WorldCat record   
Greiner’s collection of Whig songs, calculated for the meridian of the Buckeye state, and respectfully dedicated to the Clay clubs of ‘Old Muskingum’.
Publisher: Columbus : Printed by Scott and Teesdale, 1844.
Edition/Format:   Print book : English
 
Google Books
April 1845, Cincinnati Miscellany (Cincinnati, OH), pg. 240, col. 1:
Ohio,          Buckeyes.
Indiana,        Hoosiers.
Illinois,        Suckers.
Missouri,        Pewks.
Mississippi,      Tadpoles
Arkansas,      Gophers.
Michigan,        Wolverines.
Florida,          Fly up the Creeks.
Wisconsin,      Badgers.
Iowa,          Hawkeyes.
N. W. Territory,  Prairie Dogs.
Oregon,        Hard Cases.
 
Chronicling America
23 August 1845, Ripley (MS) Advertiser, pg. 1, cols. 4-5:
NATIONAL NICKNAMES.—It will be seen by the following from an exchange paper that the people of every state have nicknames, and some very curious and ludicrous ones:
 
The inhabitants of Maine, are called Foxes; New Hampshire, Granite Boys; Massachusetts, Bay Staters; Vermont, Green Mountain Boys; Rhode Island, Gun Flints; Connecticut, Wooden Nutmegs; New York, Knickerbockers; New Jersey, Clamcatchers; Pennsylvania, Leatherheads; Delaware, Muskrats; Maryland, Craw-Thumpers; Virginia, Beagles; North Carolina, Weasels; Georgia, Buzzards; Louisiana, Creowls; Alabama, Lizzards; Kentucky, Corn crackers; Tennessee, Cottonmanics; Ohio, Buckeyes; Indiana, Hoosiers; Illinois, Suckers; Missouri, Pewks; Mississippi, Tadpoles; Arkansas, Gophers; Michigan, Wolverines; Florida, Fly-up-the-Creeks; Wisconsin, Badgers; Iowa, Hawkeyes; N. W. Territory, Prairie Dogs; Oregon, Hard Cases.
 
OCLC WorldCat record
The old Buckeye State
Author: Frederick H Pease
Publisher: Cleveland : S. Brainard & Co., ©1859.
Series: New songs and quartetts as sung by the Barker family.
Edition/Format:   Musical score : English
 
Chronicling America
4 July 1860, The Spirit of Democracy (Woodsfield, OH), “National Nicknames,” pg. 1, col. 7:
The inhabitants of Maine are called Foxes; New Hampshire, Granite Boys; Massachusetts, Bay Staters; Vermont, Green Mountain Boys; Rhode Island, Gun Flints; Connecticut, Wooden Nutmegs; New York, Knickerbockers; New Jersey, Clam Catchers; Pennsylvania, Leather Heads; Delaware, Muskrats; Maryland, Claw Thumpers; Virginia, Beagles; North Carolina, Tar Boilers; South Carolina, Weasels; Georgia, Buzzards; Louisiana, Creowls; Alabama, Lizards; Kentucky, Corn Crackers; Ohio, Buckeyes; Michigan, Wolverines; Indiana, Hoosiers; illinois, Suckers; Missouri, Pukes: Mississippi, Tad-Poles; Florida, Fly up the Creeks; Wisconsin, Badgers; Iowa, Hawkeyes; Oregon, Hard Cases.
 
1 December 1865, The Rescue (Sacramento, CA),  “National Nicknames,” pg. 3, col. 3:
... Ohio, Buckeyes; ...
 
Google Books
Annual Statistician—1876
Compiled by John P. Mains
San Francisco, CA: L. P. McCarty, Publisher
1876
Pg. 90:
NICKNAMES OF STATES AND THEIR INHABITANTS.
(...)
OHIO—The Buckeye State. Buckeyes.
 
Google Books
U. S.
An Index to the United States of America
Compiled by Malcolm Townsend
Boston, MA: D. Lothrop Company
1890
Pg. 72:
NICKNAMES OF THE STATES.
(...)
Ohio…Buckeye...From the Buckeye trees {AEsculus glabra] that abound, the nut of which bears a resemblance to a buck's eye.

Google Books
Universal Dictionary of the English Language
Edited by Robert Hunter and Charles Morris
New York, NY: Peter Fenelon Collier, Publisher
1898
Pg. 5344:
Ohio. The Buckeye State (from the abundance of buckeye—horse-chestnut—trees).