Nickname: "Double Down"
Cocky, impulsive, and extremely reckless, "Double Down" Green is a perfect compliment to his husband (and superior officer), "Road Block". Where his husband prefers carefully thought out tactics and a slow, methodical plan of attack, Double Down will always choose to rush straight at the alien menace, shotgun blazing.
And he does prefer the shotgun--the rest of his squad was anxious to try out the new weaponry Dr. Vahlen and Dr. Shen had developed from alien technology, but he refused to give up his modified Benelli. Finally, Dr. Shen was able to create a "laser scattergun" that met his standards, and he upgraded to a more advanced weapon.
Major Green is notoriously impulsive--he once shot an alien at point blank range, covering himself in its acidic blood and getting severely wounding in the process. Less than a month later, he did it again. He also famously sprinted across the field of battle to attack an unwounded enemy, only to find that he had neglected to reload his weapon. He was able to fire once, wounding and enraging it, and was only saved from certain death by Lieutenant Beef Stock's timely arrival. He later claimed that his intention all along had been to beat it to death with the butt of his gun.
Green is also very cocky, and is the only soldier in the XCOM program to actively make use of the Arc Thrower neural inhibitor. This device was created in order to render enemies unconscious without wounding them, and has historically been vastly unpopular. Except when explicitly ordered to capture aliens alive, no one is willing to risk the extremely short range and the notoriously unpredictable nature of the weapon--sometimes it knocks them out, sometimes it just pisses them off.
The exception is John Green, who considers it a point of pride to always return with at least one living captive in tow. He often runs great risks to this end, and has been saved from abortive attempts more than once. He also has an unpleasant habit of yelling at his fellow soldiers for killing the enemy "too quickly" and "ruining his collection"--a frequent point of contention with Mad Man Hendricks.
Despite this, Green is very popular among the squad and generally well regarded. Even Hendricks admits that although he takes far too many risks, he has maintained an impeccable, and impressive, record.
During Operation Avenger, Double Down Green took his recklessness to even greater heights. Understanding that the fate of the world was literally at stake, he sprinted 80 feet across the throne room to shoot one of the alien high council in the face with his shotgun. Surprised to find himself still alive twenty seconds later, he sprinted another 60 feet to go toe-to-toe with a second! Against all odds, Double Down and Mad Man Hendricks both managed to survive the assault intact.