The creativity in my brain has logged out for the night so I can't think of a name for the generation I belong to. Generation Z and Post-Millennial have been used for a few years, labels affixed to us regardless as to whether they fit, and they sort of seem stuck now. One of my friends actually started a successful Generation Z consulting firm and even though he dislikes the name, he continued to use it because it's what's most identifiable. Both seem more like addenda. Though, the quest to decide on a name for a generation isn't unique to mine....whatever mine is. In a 1994 college commencement speech Kurt Vonnegut told the graduates, "Now you young twerps want a new name for your generation? Probably not, you just want jobs, right? Well, the media do us all such tremendous favors when they call you Generation X, right? Two clicks from the very end of the alphabet. I hereby declare you Generation A, as much at the beginning of a series of astonishing triumphs and failures as Adam and Eve were so long ago." I actually kind of prefer Generation A instead of Z, and it feels more fitting for a generation that is the first to grow up in the new millennium.
Anyways, so the Vonnegut quote is in the epigraph to Douglas Coupland's
Generation A, which was written in the 2000s in the same format as his early 90s book
Generation X: Tales for an Accelerated Culture. The bookended generations have commonality in their perspectives; it's mainly their technology that sets them apart. At that time he wrote X he said that it was for people his age who were born in the 1960s and were sick of stupid labels, sick of being marginalized in lousy jobs, and tired of hearing about themselves from others. That's a sentiment that I think basically every generation has had. Anyways, so the irony of it is that he was sick of labels, and yet he inadvertently popularized the labeling of his generation as Gen X. And by doing that, it inevitably lead to Y (until that was replaced with "Millennial" and now Z. At least he didn't start with A, or we'd now be known as Generation C.
Edit:
I'm not fond of the name but I sort of

what she said anyways:
The oldest respondent to give her age was 91-year-old Annette Benedict, of the Bronx. “I figure you’re not an ageist,” she wrote, a gambit that all but ensured her inclusion. Her suggested name was The Thumbies, for the digit used to operate smartphones. “I think that suits them,” she said, chuckling, when I called her.