Nope, the Browns are named after the owner of the Bengals.
Washington Vampires
Washington Pedos
Washington Ticks
Washington Virus
Washington Mosquitos
Washington Degenerates
Washington Cabal
Washington Leeches
Washington Disease
Washington Insiders
Washington Bribery
I mean, this isn't a mystery, it was named after Paul Brown, and then they kicked Paul Brown out a few decades later.