European football must have been well known for quite a while and is primarily played using the foot. So why did inventors and early participants in American football choose to name their sport Football, when A) there was already a sport named football and B) the sport is mostly played using hands
I wrote about the origins of the American game a long time ago and although it doesn't specifically touch on decisions about the name, the underlying answer should, I hope, make it clear, namely that the game wasn't "invented" out of nothing, but instead evolved over time, and can be seen as a "Football Code", same as Rugby League and Union Footballs, Association Football, Aussie Football, etc.