Trey (yes, it is pronouced Tray) is a three on dice or cards. One of our little neighbor kids is called Trey. It is not his given name but his dad must have been a II and he a III so instead of calling him the same name as his dad, they call him Trey.
Sorry it doesn't have the firefighter connotation unless them dudes play a lot of poker in their down time.

What about "Captain", "Chief" "Sarge"...don't firefighters have some sort of rank like the military? What would be the low man on the totem pole 'cause we wouldn't want him coming in like he was the boss of anybody?
Sorry, Cinder, I know you are narrowing the names down, but I just can't stop myself.