Usually any school titled using the state name is a public university...it doesn't have to include the word "state". Michigan, Minnesota, Illinois, Indiana - all public universities...also UCLA, Texas, Kentucky, N.C. State, Florida, and Florida State are public. Then some public universities are not named after the state, like Clemson and Auburn universities. Sometimes schools with the state in their name are private too, like USC (Southern Cal).
Sometimes universities named for the city are public - like the University of Memphis, U. of Louisville, U. of Cincinnati and U. of Houston - but there are also some that are private, like the University of Chicago, Miami, and Syracuse University.
So I guess there is no definite rule to the naming of a university...any private or public university can be named in whatever manner they choose.