What was the name of the U.S. policy that aimed to slow the spread of Communism in the world?
It is known as Containment.
As the name suggests it was a policy of trying to contain the spread of communism in the post 1945 world. This was reflected in the formation of NATO and the Marshall Plan to regenerate Western Europe economically.
It can also be seen in The Domino Theory which argued that if one country fell to communism, neighbouring countries would too. This was a key element in US foreign policy in South East Asia.
Containment can also be applied to US foreign policy in Central and South America although this can also be seen as an extension of The Monroe Doctrine. Successive American governments supported numerous dictators and brutal governments in countries such as Nicaragua, Honduras , El Salvador and Cuba in order to prevent a perceived threat from the left.