What was the name of the theory that said that if one country in a region fell to Communism, others would surely follow?

The correct answer is domino theory.

The domino theory was a geopolitical theory that suggested that if one country in a region fell to communism, neighboring countries would also fall, like a row of falling dominoes. This theory was particularly influential during the Cold War, shaping U.S. foreign policy and intervention strategies in various regions, particularly Southeast Asia.