State is the name of the University, they have many of them in each State.
Example - Georgia State University is not University of Georgia (Bulldogs). Alabama has multiple big ones, as does Texas and Florida. In fact, the Southern States have lots of teams that are well supported and they don't always tie-up to the biggest Cities. Alabama is in Tuscaloosa I think, not Montgomery, and Auburn is a small City of about 60k people.
For sure, I understand that but in the most part they will still be covering fairly large catchment areas but there is more "pride" in the US so to speak - even if we correlate a UK/European level of pride to State level.
Of course I know that you'll have a much better understanding, since you do live over yonder way