In Metal Gear Solid 3: Snake Eater, Naked Snake’s military unit is FOX.
FOX is a special operations unit associated with the CIA in the game’s 1964 Cold War setting. Naked Snake is deployed as a FOX operative during Operation Virtuous Mission and later Operation Snake Eater. His codename is Naked Snake, while FOX identifies the unit he serves.
This distinction is important because the Metal Gear series uses several related military names. FOXHOUND is a later special forces unit connected with characters such as Solid Snake, while FOX is its earlier predecessor in the series’ fictional history. CIPHER and the Patriots are intelligence organizations, not Naked Snake’s field unit in this mission.
The game’s unit terminology also connects Snake Eater to the broader origin story of the franchise. Events involving FOX, Major Zero, and Naked Snake help establish the political and military foundations that later lead to organizations seen in subsequent Metal Gear Solid games.