I started living in Columbus in 1980, my dad a professor at OSU. Everybody just said OSU. Around 1985-86 I remember reading a memo sent out saying they wanted to emphasize “The Ohio State” to differentiate between Oklahoma State and Oregon State which were also OSU. I thought it sounded stupid, everyone just said OSU before then even though “The Ohio State University” had been the official name since it’s inception back in 1878.
I don’t think it caught on at first until you started seeing NFL players introduce themselves as “Eddie George” “THE Ohio State University” before NFL games for example back in the 90’s.
Love it or hate it, it does separate them from the other OSU’s.