It was named the cold war because the two countries who contributed the most never actually fought each other. America mostly helped other countries with supplies needed to fight against The Soviet Union. They never actually met on the battlefield.
So called because it never boiled over into open war between the two powers but was focused on espionage, political subversion and proxy wars. Western Europe and Japan were rebuilt through the American Marshall Plan whereas Eastern Europe fell in the Soviet sphere of influence and rejected the plan.
