Snake was found wandering the wastelands by Brotherhood scouts. It transpired that there had been a spate of robberies in his old village. Snake was the culprit. He had two choices; starve to death in the wastelands or have both hands removed. It turns out he has a third choice, serve the BoS.
Snake is clearly inspired by anti-hero Snake Plissken from the films Escape From New York and Escape From L.A.. In addition to their name, they also have similar backstories, skills, and physical appeareance.