The Manager of the Year Award did not gain sanction from the BBWAA until 1983. Until then, the Associated Press, the United Press International, and The Sporting News all had their own awards for managers. Often, three different managers would be named. But the BBWAA Award is now considered the official Manager of the Year Award.
2020 National League Manager of the Year

Don Mattingly, Miami Marlins
2020 American League Manager of the Year

Kevin Cash, Tampa Bay Rays