My email address was/is @ohiou.edu. I'm pretty sure when I was applying, our primary web address was
www.ohiou.edu. Both my wife and I are "used" to our institution being called Ohio U.
Out here (Kansas) if we say "OU" it's Oklahoma. And if we say "the other OU" it's Oregon. And if we went to "Ohio" then "well, that's an interesting place to go visit." Only when we went to "Ohio University" or "Ohio U" does it click in their heads.
And even then they're confused about the other schools... up until a few years ago it was "we're the ones that are not known for playing sports."
I say things are better now. They at least know who Ohio U is.
SP