Fame
As a baseball manager, you've already got an entire city full of people prepared to praise or loathe every single decision you make. Whether you receive any national recognition for those decisions is a whole different ball...game...
Sorry, we walked straight into that one. Couldn't miss it.
Most famous managers have one thing in common: their teams win, and win a lot, especially the big ones. If you want to get famous, win the World Series a whole bunch of times. One championship will get you some coverage, but three will make you an icon.
If you can't manage a bunch of wins, you can always aim to be a sore loser instead. Cultivate a temper that often results in epic tantrums when a call doesn't go your team's way. Kick the dirt, throw your hat, and get in an umpire's face—it's all instant fodder for the interwebs. It may not be right, but it'll probably get you featured on SportsCenter.
There's a final way to get famous as a manager, but you won't like it. You could manage an abysmally, historically terrible team. If you never win a game, you won't have a job for long, but no one will forget the coach who went 0-162.