Gray Fox, current code name unknown.
One of his first steps was bureaucratic: to shift control of an undercover unit, known then as the Gray Fox (it has recently been given a new code
name), from the Army to the Special Operations Command (socom), in Tampa. Gray Fox was formally assigned to socom in July, 2002, at the instigation of
Rumsfeld’s office, which meant that the undercover unit would have a single commander for administration and operational deployment. Then, last
fall, Rumsfeld’s ability to deploy the commandos expanded. According to a Pentagon consultant, an Execute Order on the Global War on Terrorism
(referred to throughout the government as gwot) was issued at Rumsfeld’s direction. The order specifically authorized the military “to find and
finish” terrorist targets, the consultant said.

Source:
www.newyorker.com...
I doubt it is the most secret unit in the world, there are probably a few that don't exist to us yet.