The name is from a book Fugazi front man Ian MacKaye was reading called "Nam" by Mark Baker. Ian says:
"It's a book of reflections of Vietnam veterans and at one point, this guy said everything was 'Fugazi.' I looked it up in the glossary and it said, 'fucked up situation.' It was right at the point when we were getting ready to do our first show and I was desperately trying to come up with a name, anything other than Ian's New Band."