Rising

The following definitions are taken from dictionary.com
1. Next: immediately following in time, order, importance, etc.: the next day; the next person in line.
2. Rising: growing or advancing to adult years: the rising generation.
We are not the next generation. The next generation has not been born yet. If you need to call us something, don't bother with cutesy names like "Millenials" or "Generation Y". Generations are fuzzy categories anyways. Two of my brothers were born in 1999 and 2002. If you view January 1, 2000 as the cutoff date, they're different generations.
Just say the rising generation.