We didn't come up with the name "Soccer." Soccer is actually a slang term for the real name of the sport, "Association Football." People around the world still use the term, although it's obviously fallen out of favor.
The term "football" doesn't mean what you think it means. Football is an antiquated term that refers to a working-class sports game. They are games you play on your foot, as opposed to the games nobility played, like Polo. "Football" as a term is synonomous with "sports." Baseball is a football game, hockey is a football game. Ironically enough, even basketball is a football game. We really didn't name our sport "football," it was more like an unnamed college sport, and all sports were called "football." As the practice diminished, the name stuck for that sport. The real name for the sport is "Gridiron Football."