i found this on their site:
A few people asked about our name and the song "Edward." There is NO connection. We've been a band since 2004, have never seen any of the movies or read the books, and "Edward" is a referrence to Edward Scissorhands, not Twilight. We would've called the song Scissorhands, but I think there's a Mars Volta song called th...at. That song was written like a year and a half ago before the Twilight movie started getting hype.