People born between 1980 and 1995 (or so) were the last ones to be born last millennium, and Z is the last letter of the alphabet, and people born one generation later were born this millennium or within the last 5 years (or so) of last millennium, so why wouldn't it be Gen Z, then millennials?
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Favorite Answer
The nickname for Gen Y is the term Millennial. Gen Y is our technical name. So it went Gen X, Gen Y, Gen Z. They just followed the end of the alphabet, the lazy sods.
Foofa
Because we're always having to come up with new names and even the names you've listed aren't necessarily the ones everyone uses. There are also groups between those groups that sociologists use to get more granular on the trends and norms of certain age groups, i.e. "xennials" and such.