Unless the goal of the Cold War was simply to dismantle the Soviet Union and its closest allies, I don’t think that it’s perfectly accurate to say that it ended (in either the 1990s or elsewhen).
The anticommunists continued to struggle against popular communist parties in the Russian Federation and elsewhere, they are trying and failing to dismantle the Democratic People’s Republic of Korea and the Republic of Cuba, the liberal reforms in the People’s Rep. of China and the Socialist Rep. of Vietnam were poor substitutes for overthrowal, and so far the anticommunists haven’t balkanized the Russian Federation.
If we view the Cold War as essentially a complex class war (which would be quite reasonable), then it certainly never ended, or even been on pause.
Recently I’ve been asking myself if the Cold War ever started or existed. Did the USSR even refer to it (by this name or any other)?
It’s the war against communism. The USSR had been attacked ever since Lenin, and China was attacked ever since Mao. WW2 just put things on hold because there was a bigger primary contradiction.