What is the Best Name for Members of This Generation?

What I have noticed is that researchers, the media, and people in general refer to the generation whose first members were born around 1980 (plus or minus a year) as Gen Y, Millennials, Twentysomethings, Nexters, and other names that are best unmentioned.  So which one is correct?

I use the moniker “twentysomethings” on this blog.  However, the members of this generation won’t always be twentysomethings.  So while that title works today, we may need a more permanent one.

I would rule out “Nexters” because like twentysomethings it will not endure.  It will only work until the “next” “nexters” come along.  The folks over at Generational Differences Consulting vote for “Millennials” as the name of choice.  In fact, on Twitter.com today, they state that they are on a mission “to get unknowing people to stop using Gen Y for Millennials”.  They claim that this new generation is not a repeat of Gen X.  Instead they are truly unique.  I tend to agree that Millennials – because the first members of this generation came of age at the time of the new millennium – is a good choice for an enduring title.