I would agree with the above answer. The only way we can really refer to it as the Vietnam Era is to associate tension between the superpowers with Soviet communist expansion vs. American and allied containment policies. The French fought an anti-communist imperial war in Vietnam from 1945 - 1954. Soon after the French lost, America moved in with aid, then advisers and troops in the 1960's.
But this expansion vs. containment tension played out around the globe in those two decades, in places like Korea, Africa, and Latin America. I would agree the only accurate name to describe the tension of that time period overall is the Cold War.
No, I wouldn't call this the Vietnam Era. I would call this the Cold War. The Vietnam Era is not usually said to start that early. However, neither the "Cold War" nor the "Vietnam Era" really completely fits this definition.
The Cold War lasts from more or less the end of World War II until about 1990, so it is much longer than just the two decades you mention. But "period of tension between the superpowers" describes that time period quite well.
When we talk about the Vietnam Era we usually are referring to the time from about 1963 to 1973.
The period that you mentioned was called "The Cold War." During the period of the Cold War, the two countries had a strong sense of distrust towards one another. America had used the Atomic bomb during World War II so there was a strong tension that the bomb would be used again. It became a time of rapid progression in the building of nuclear weapons.
In America fallout shelters were established and school children grew up being taught how to cleanse water and what to do if Russia launched weapons at America. The United Sates also experienced conflict between Russia has the county tried to overtake other regions.
A great struggle remained in the aftermath of World War II, between democratic capitalism and communism. This helps to explain why some Western commanders, notably American General George S. Patton, urged that the Western Allies not stop at the Elbe but continue on through Germany and attack the Soviets. That suggestion was not taken seriously, but another general’s plan, that of George C. Marshal, for economic assistance to war-torn Europe can be seen as a subtler way of winning that area for democratic capitalism. As all this implies, within a few years of the war, the victorious Alliance, Europe, and the world divided into two opposing camps, fighting a life-and-death struggle with propaganda and materiel, as well as bullets, a sequel to World War II known as the Cold War.
Finally, if World War II settled anything, it was the rise to preeminence of the two great superpowers, The Soviet Union and the United States, who would be the principal combatants in the Cold War.
Obviously, the end of World War II left much unfinished business. Much of Europe, China, and Japan were devastated. Whole cities had been leveled by successive bombing campaigns. Armies of refugees found themselves displaced. Local governments broke down as the defeated regimes crumbled. The Allies turned from occupiers to administrators and judges. Germany was divided into four zones, corresponding to the British, the French, the Americans, and the Russians. And once that territory was divided, it was a race between the superpowers to divide the rest of the territories that were left in ruins.