NO he's not, there are 4 snakes. 

The first is Solid Snake the son of Big boss, Aka Naked snake, Aka Venom Snake, Aka Punished Snake 

The second is Liquid Snake, the twin of Solid snake with blonde hair and a british accent, also he get's his ass whooped alot. 

The third is a clone of Big boss Aka Venom Snake, Aka Naked Snake, made to look like the man and talk like him, but lose like Liquid snake. 

The last and most badass, Big boss, killer of The Boss, Aka the mother of Special forces. He was the most toughest of all the Snakes being able to lose to Solid snake many times and bounce back even when he gotten older, and died from Fox die next to The Boss' unmarked grave. 

So he's not Solid Snake he's the mother fucking BIG BOSS, AKA VENOM SNAKE, AKA PUNISHED SNAKE.