It's 85 miles from Lexington to Cincinnati (you must drive fast). It used to be that a company would seek to name a stadium near their HQ (Valvoline is in Lexington). Mercedes Benz in Atlanta, Levi's Stadium with the 49ers, Raymond James in Tampa, MetLife in NY/NJ. I don't think Kroger will get the mileage that other companies have received for their sponsorship dollars.
The Kroger Grocery Chain is located all over KY, IN., OH., and W.V. The only point I am making is that it is a familiar brand in those states, major conference and UK basketball.