This happened Sunday night.
Can't remember what my girls and I were watching on TV, but Dara (14 years old) suddenly asks "What are baby boomers?" and I explain it. Dara asks why they call people that and I explain demographics and the different groups. I tell them how their grandpa was in the G.I. Generation, their grandma is in the Silent Generation and their uncle is a Baby Boomer. I am Generation X.
I tell both Taylor (16 years old) and Dara that they are part of Generation Y. Taylor says "I'd rather be a part of Generation Z. It sounds cooler." (She learned a little bit about demos in school.)
We chatted a bit more, and Taylor's overall take was this: Each person is different, and even though she can see how large age groups can have life experiences that shape their thoughts and opinions as a whole, she's cynical about companies that make assumptions based on generalizations (she didn't say it exactly that way, but that was the gist of it.)
That's why I believe terms like Gen Y should be kept as internal labels—instead of product or website names—because they are labels. And no one really likes to be labelled.