Business Insider has a pair of articles about generation nicknames in the USA and the rest of the First World, and (conversely) nicknamed generations. The first discusses a Goldman Sachs report that attempts to characterize the members of "Generation Z". If you're a bit challenged as far as remembering exactly what age groups these nicknames refer to, the piece has an excellent chart breaking out the generations by age [businessinsider.com], and then by population count (in the USA). Details of Goldman's Gen Z portrait are sketchy, but it seems that one point is that GS previously seemed fascinated by the Millenials [goldmansachs.com], the generation that came before Gen Z.
The second article is a proposal by demographer Mark McCrindle for the nickname of the new generation [businessinsider.com], whose early members are being born as you read this.
Coincidentally, TIME is running a story on how the generation nicknames came about [time.com]; I was surprised to see longtime NBC news anchor Tom Brokaw being credited with coming up with the 'Greatest Generation' moniker. An older article (from googling) covers similar ground. [esds1.pt]