What was the name given to the idea that if vietnam fell to communism, the rest of southeast asia
would become communist?

This was known as the Domino Theory.

The term was coined during the presidency of  Truman and his Truman Doctrine.

The Truman Doctrine during the Cold War focused on a policy of containment of Soviet Union. The Domino thoery believed that if one country fell under the influence of the Soviet Union, it will pave the way for others.

The Truman Doctrine was publicised ont he 12th of march, 1947 and ushered in an Era of extreme competition between the United States and Soviet Union.

Many Scholars attribute the Vietnam War to the United States policy of containment.