I mean, the linked Wikipedia article literally describes for many of them who coined the terms and, in some cases, why. “The Greatest Generation” is the title of a contemporary book about the people who fought in World War 2 (and their cohort), and the name became popular as a way to describe people of that cohort.
For those wondering, this is from “Science: Abridged Beyond the Point of Usefulness”, by the inestimable Zach Weinersmith.