Contra was born in Japanese arcades in 1987 under the name Gryzor. When the game proved to be a smash, it was quickly ported over to U.S. arcades and redubbed Contra.
It's probably tired trivia at this point, but the Contra name was born out of two Japanese kanji symbols on the side of the cabinet that were pronounced "kon" and "tra". The name stuck and has been used for every version of the game since.