Snake's real name is David. However, he is more commonly known as Solid Snake.
While "Solid Snake" is the name he primarily uses, and is how he's known throughout the Metal Gear universe, his actual birth name is David. He is a clone of Big Boss, and like his "brothers" Liquid Snake and Solidus Snake, uses the codename "Snake" rather than his given name.
Therefore, the answer to what is Snake's full name, based on the reference provided, is David.
