Billie Joe Armstrong, Mike Dirnt and Al Sobrante (aka John Kiffmeyer) happened to be watching an episode of Sesame Street, where the character Oscar the Grouch happened to exclaim, "I'm having such a green day!" In his case, it only mean spending the whole day lazing around at home, but the actual meaning included smoking weed. Since Sweet Children were avid pot-fans, that sentence by Oscar influenced them to change Sweet Children's name to Green Day. Also, there was another band floating around called 'Sweet Baby' and Larry Livermore, Lookout! Records' owner didn't want any confusions.