His name is Vash the Stampede a mysterious and terrifying Legend on Gunsmoke. So far there is no direct explanation for this title or name. It is my guess that either he was conscient of being "Vash" when he was born or that Rem gave him that name. As for "The Stampede" it is probably something given to him by the folk of Gunsmoke after hearing of his terrible reputation for destruction.
A.K.A:He is also known as "The Humanoid Typhoon" and "The 60 Billion Double Dollar Man". The first one he got off of reputation just like his "Stampede" title, but the second one he got after recieving a bounty of 60 billion double dollars on his head, dead or alive. Lina and her "Grandma" in episode 18, "Goodbye For Now" called Vash "Ericks". Vash had been reocvering from the Fifth Moon Incident during his time with lina, but it is not known weather she was the one who gave him that name or if it was a name Vash used to prevent trouble. Nicholas D. Wolfwood also gave him the nickname of "Tongari", translated into "Needle Noggin". This along with the other common nickname of "Broom Head", used often by Meryl refers to Vash's spiky hair style. There are many other less notable names and titles given to Vash by different people, but the ones above are the most important.