There's no official nickname for the unit yet. The unit consists of volunteers (and there were a lot of volunteers) and has a 22 man headquarters, 30 reconnaissance Marines (mostly from the existing elite Marine Force Recon units), 28 intelligence specialists and what is described as "a six-person team to provide firepower."
The official job description calls for the Marine commandos to perform four types of jobs; special reconnaissance (which Marine Force Recon have been doing for a long time); combat strikes (your classic commando raid); internal defense of foreign nations (bodyguards for key people or protection of vital installations); and support of international coalitions (which covers just about anything.) Knowing the Marines, the unofficial job description is probably more like; "Anything, anytime, anywhere."
The U.S. Marine Corps is forming its first commando unit, the 86 man Marine Corps Special Operations Command Detachment. The unit will begin training in June and be ready for action in April, 2004. The formation of the unit is a direct result of the War on Terrorism. If the first unit is successful, another may be formed. The unit will be the first Marine contribution to the Special Operations Command (which has commando units from the army, navy and air force.)