Picking Your Central Banker

How does Alan Greenspan get to be Alan Greenspan (He recently put the dismal into the dismal science - - "There is nothing out there that I can see which will alter the trend or the level of unemployment in this country.")? How does a country pick its central banker - - maybe one of the most important unelected positions in any democracy? John Paul Rathbone, in his The Sugar King of Havana (2010), points out how Fidel Castro picked his first central banker in post-revolution Cuba:

Guevara certainly made for an unlikely central banker. He loved telling the story of how he got the job. Supposedly, at a cabinet meeting to decide who should be the new bank governor, Fidel Castro had said that what he needed was a "good economista." Guevara stuck up his hand, much to Castro's surprise. "But Che, I didn't know you were an economist!" "Oh, I thought you said you needed a good comunista," Guevara replied.