What is the name of the G.I. Joe team's underground base?

The G.I. Joe team’s underground base is called The Pit.

The Pit is the team’s secret headquarters and base of operations in the classic Marvel comic continuity. Its original incarnation lies beneath the motor pool of the Army Chaplains’ Assistants School at Fort Wadsworth on Staten Island, New York, allowing the Joes to conceal a sophisticated military installation in an ordinary-looking location.

The underground complex includes vehicle and weapons storage, communications and briefing rooms, training areas, an armory, living quarters, computers, generators, and classified records. The original comic-book blueprint describes five levels, making The Pit far more than a simple bunker.

Different continuities and stories use more than one facility known as The Pit. Later versions relocate or rebuild the headquarters, and the 2009 film gives it a desert setting with training technology and concealed exits. “The Vault,” “The Bunker,” and “The Fort” are descriptive-sounding names, but they are not the canonical headquarters name.