Football franchises move around, and it was the Rams who represented Cleveland before moving to L.A. and then to St. Louis.
In 1946, when the city was given a franchise in the AAFC, they held a contest to name the new team, and the winner was the Brown Bombers, after the great champion Joe Louis.
However, the name was color sensitive for the time, and so they compromised by naming the team the Browns after coach Paul Brown.