Direct quote
“That is how I got the snake part. I guess the slithering of the snake is definitely not a solid motion. It's smoother, more liquid. I also wanted to create a paradoxical name.”
What it documents
Asked where his character names came from, and specifically the name Solid Snake, Kojima said they came from 1997: Escape from New York; he said that from that film he took the "snake" part, that the slithering of a snake is not a solid motion but smoother and more liquid, and that he also wanted to create a paradoxical name.
Source
Gamers Today, interview with Hideo Kojima (undated page, retrieved from web.archive.org). View source ↗
“GT: You came up with some pretty unique names for your characters in Metal Gear such as your hero, Solid Snake. Where'd you get these names? HK: From Escape From New York.”