"The" was made officially part of The Ohio State University's name when it changed from Ohio Agricultural And Mechanical College.
Actually they tried to trademark THE, which was denied. The trademark was for a line of "THE" clothing. Part of the reasoning may be Marc Jacobs had already applied for a trademark on "The" related to clothing. OSU's filing may have be defensive in nature as licensees have been selling t shirts and hats with "THE" for a while; and could wind up losing the right to sell such items if mJ gets a trademark and decides to sell similar items.
Trademark issues for school logos and identifying marks are not unusual, for example Ohio State and Oklahoma State came to an agreement over the use of OSU; a move necessary to protect the respective trademarks. Generally they come to an amicable agreement to protect the trademarks so they don't lose them. Notre Dame forced a small high school to stop using a fighting leprchaun as a mascot. Ohio State sued Caesar's over "The Shoe." Texas A&M vigorously defends "The 12th Man." "THON" is a registered trademark for the Penn State IFC/Panhellenic Dance Marathon. It's not just the big ones, Mount St. Mary’s University in MD sued Mount St. Mary’s University of Los Angles when they changed their name to University from College.