Outside of buying tickets to the Bengals games to help avoid a sell out, I don't believe P&G or Kroger do much with the Bengals. If they do, they shouldn't be because I am a Bengals fan that lives outside of Cincinnati and their companies never cross my mind when I think of the Bengals. Paul Brown Stadium is not being renamed. Neither is Great American Ball Park (which is already corporately sponsored). So, actually, if you want naming rights in the city of Cincinnati and you are a Fortune 500 company, your option is a new basketball arena for UC. Hey, if 5/3rd wants to pony up money, I am for that too. Point is, just because there are pro teams in town, it doesn't mean that there aren't companies with money who could spend it on UC. 30+ games a year on National TV (ESPN or CBS SportsNetwork) is pretty darn good exposure.
Oh, and last time I checked, Yum doesn't get any extra exposure because it is the "only game in town." They play just as many games as UC and have the same number of opportunities for people to see the name "Yum" on television.