Yes, I know it's not technically just methane, but methane is its primary constituent.
"Fossil gas" is also probably a suitable term, but I like "fossil methane" because it gets that spooky chemical name benefit.
It's called natural gas because before we got it from the ground we got it by heating coal until it gave off gas and piping that to homes and businesses.
Natural gas is natural because it naturally occurs in the earth and is not distilled from coal like coal gas is.