In fact, MLB has also never had a player whose last name was the same as the city he played for. Maybe if Daryl Boston had played for the Red Sox or Reggie Cleveland had pitched for the Guardians, then at least one player could have had the same name on both sides of the road jersey.
Now, the Cleveland Naps do sort of fall into the "Browns" category in that they were named after a player. But they went with the abbreviated first name...