Recently Suggested Names:
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Green Beacon
Green Lantern
Green Lotus
Green Times
Green Flash
Green Herald
Green Planet
Green Epoch
Green Onion
Green Vision

and here's my own creation after a couple of glasses of Alexander Valley Merlot:
"The Opiate of the Green Masses" (it's a joke of course :-)

Previously Suggested Names:
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I put a * next to the ones that we seemed to like best.

* Green California (Glen Mowrer)
Green Movement (Michael Stanley-Jones)
Green Vanguard (James Rickabaugh)
Why Should I vote Green (Lawrence Rockwood)
InForum Green (James Murphy)
Green Party News (Aaron Lipke)
Green Party Tribune (Aaron Lipke)
Green Party Recycler (Aaron Lipke)
Green Light (Karen Spence)
* The Green Light (Gary Waayers)
Verdant (Greg Bird)

The following two names refer to the Sunflower genus/species:
Asterace (Greg Bird)
Helianth (Greg Bird)

The Green Tatler (Lupita Jimenez)
The Green Crier (Lupita Jimenez)
Solar Green (Lupita Jimenez)
The Green Light (Lupita Jimenez)
Soleil (Lupita Jimenez)
Le Tournesol (Lupita Jimenez)
The Green Parasol (Lupita Jimenez)
Sunflower Tatler (Lupita Jimenez)
Sunflower Seeds (Lupita Jimenez)