Cold War II/Is official declaration required to start a Cold War?

From what I have learned, the Cold War was never officially declared by all sides, including the United States and the Soviet Union. Rather a "cold war" was created and then popularized in multiple sources, like newspapers, media and and academia. This leads me to wonder whether Cold War II can happen as unofficially declared. Heightened tensions can be considered signs of heading toward another "Cold War", but very few sources at this time connect Cold War II to other events.