The Cold War greatly affected America's identity, as we became a nation obsessed with preventing the spread of communism and competing/trying to beat the Soviets in our technological advancements.
A perfect example of this would be the foreign policy adopted during this time, known as containment. Ultimately, the US federal government was trying to stop the spread of communism from the Soviet Union to other European countries. To prevent this from happening, the US gave countries economic aid through things like the Truman Doctrine and Marshall Plan.
Along with this, the US also got involved in multiple overseas wars to stop the spread of communism. This included the Korean and Vietnam War. In both scenarios, the US was trying to stop the spread of communism from the Northern part of the country into the Southern part of the country.
Besides stopping the spread of communism, the US was focused on developing better technology than the Soviets. This was especially true after the Soviet Union launched Sputnik 1 into space. This resulted in the Space Race, and the American education system becoming obsessed with advancement in math, science, and engineering.
