Per the Ohio State Library.
Why are we called "THE" Ohio State University"?
In 1986, a new University logo was introduced in the hopes of moving away from the "OSU" symbol, which had been used since 1977. The change from simply "OSU" was said to "reflect the national stature of the institution." University officials wanted the institution to be known as "The Ohio State University," again, since OSU could also mean Oregon State and Oklahoma State University.
However, the "The" was actually part of the state legislation when the university was renamed in 1878. The following excerpt is from the Board of Trustee minutes:
"...the educational institution heretofore known as the 'Ohio Agricultural and Mechanical College,' shall be known and designated hereafter as 'The Ohio State University.'"
Those who wanted the name change thought the original name was too narrow in scope, and that it was inadequate for the institution that was the only beneficiary of the land grant act. President Edward Orton was insistent that a new name would separate the institution from other colleges in Ohio.