What is the name of the mission in Metal Gear Solid 3 that gives the game its subtitle?

The mission is called Operation Snake Eater.

Operation Snake Eater is the central mission assigned to Naked Snake in Metal Gear Solid 3: Snake Eater. Set in the Soviet Union in 1964, it requires Snake to rescue the scientist Nikolai Sokolov, eliminate the rogue Soviet officer Colonel Volgin, and stop the Shagohod project.

The operation’s name gives the game its subtitle and also connects to the game’s survival theme. Snake must eat food from the environment to restore stamina, making hunting and resource management part of the mission’s practical challenges. The title therefore works both as a military operation name and as a reference to the protagonist’s wilderness survival.

Operation Snake Eater should not be confused with Operation Virtuous, the earlier mission in the same game. Virtuous Mission ends in failure after Sokolov is recaptured and The Boss defects. Snake Eater is the follow-up operation launched to correct that failure and resolve the political crisis.