In a column about Fifth Third Bank (What gives with Fifth Third Bank? - The Straight Dope), Cecil ruminates on the reason banks would use their names to admit they were late to the game:
“We concluded that in the 19th century, bankers (and church elders) were immune to the shove-to-the-front-of-the-line mindset that curses our times and instead cheerfully acknowledged their place in the natural order of things.”
Thing is, this wasn’t just a 19th century thing, and not just for banks and churches. Cleveland spent much of the early decades of the 20th century referring to itself as the Sixth City (http://www.oldandsold.com/articles33n/american-cities-12.shtml) or Fifth City (http://images.ulib.csuohio.edu/cdm/ref/collection/postcards/id/1504), both boasting of its status based on population.
Also, on the bank front, while Cincinnati may have ended its string at five, there are even humbler institutions. New York and Philly, at least, had Sixth through Tenth National Banks; that’s as far as I bothered to Google.