A report from Pew Research purports to reveal ignorance among young people about what they are.
Pew asked respondents to identify the generation with which each identified, and sorted them by their "actual" generation. Obligatory reminder, to DiPrete's point: There is no "actual" generation for any group besides the Baby Boomers, which is a statistically defined group. Pew's definition of what counts as millennial — defined by year of birth — isn't the same as other organizations'.
That said, millennials were less likely than other groups to identify as their "correct" generation. (Wearing out my scarequote key here.)
Talk of "generations", at least since the boomers, is marketing. It's part of an advertising-tangled vision of universal popular culture, cultivating a market's greatest possible extent. Younger people don't live in that world. The idea of there being a sequence of homogenous, simply-defined monocultures is irrelevant now. So of course someone who never experienced it will just tell you which choice they like best.