http://en.wikipedia.org/wiki/Green_Day_discography
See, I read your first post and thought you were incredibly stupid for thinking that "Warning"'s 1997 release constituted "early" Green Day. Turns out it was just a fluke in my memory; you're actually incredibly stupid for thinking that "Warning"'s
2000 release constitutes "early" Green Day.
So, to answer your question, your best band name idea would be:
"Probably born in the 90s"
You can call your first album "Bad Understanding of Chronology". Most of the songs should incorporate lyrics explaining how you learned in early 2005 that Green Day had other albums than "American Idiot" while most of your friends didn't know that until later in the year.