Old Man White
Is it a coincidence that the oldest, most veteran man of the group gets the name Mr. White? His hair may not have gone too gray yet, but there's no doubt that he's the old man of the (surviving) group. White's the least amused guy at the diner. He isn't really feeling Brown's sexual interpretation of "Like a Virgin." When Blue asks, "How many dicks is that?" White says, "a lot" with a nice little eye roll thrown in for good measure. He's a grown-up.
White plays the role of a father or mentor to the younger Orange. We see this throughout the film, even in the diner scene where White and Orange are sitting next to each other and Orange at one point even has his hand on the back of White's chair, and vice versa. White's there with Eddie and Joe for Orange's bathroom story, and after the meeting, White and Orange sit in a car and talk about the plan. White gives him the rundown on how to handle uncooperative employees and customers. You can see the camaraderie in the scene.
Soft on the Inside
We learn later that White shared some personal info about himself with Orange despite Joe's prohibition. He really chafes under this whole anonymity requirement. When he's with Pink in the abandoned funeral home, he wants to tell him his name. He wants to engage.
White shows a mind-blowing amount of compassion when Orange is shot. He holds his bloody hand and tries to calm him down and talk him through the pain. He even tells him his real first name:
PINK: What was telling him your name when you weren't supposed to?
WHITE: He asked. We had just gotten away from the cops. He just got shot. It was my fault he got shot. He's a f***ing bloody mess. He's screaming. I swear to God I thought he was gonna die then and there. I'm trying to comfort him, telling him not to worry, everything will be okay, I'm gonna take care of him. And he asked me what my name was. What was I supposed to do, tell him I'm sorry, I can't give out f***ing information? It's against the rules? I don't trust you enough? Maybe I should've but I couldn't.
Once White gets them to the funeral home, he carries Orange inside and lies down with him. He holds him, whispers to him, combs his hair, does just about everything he can. It's a very tender scene, a counterpoint to the horror all around them. At one point it almost looks like he's about to kiss his head.
During the entire time at the funeral home, he's pleading for someone to get Orange some medical attention. He won't leave Orange alone. He's relentless about it with Pink and later even with Eddie, who's got other stuff on his mind:
WHITE: What are you gonna do about him?
EDDIE: Jesus Christ. Give me a f***ing chance to breathe. I got a few questions of my own here.
WHITE: You ain't dying. He is.
EDDIE: All right, Mr. F***ing Compassion. I'll call somebody.
EDDIE: A f***ing snake charmer! What do you think? I'll call a doctor. He'll fix him right up.
Orange isn't the only one White worries about. Even though he's done his share of beating up Marvin, he doesn't want to leave him alone with Blonde.
WHITE: We can't leave these guys here with him.
EDDIE: Why not?
WHITE: 'Cause he's a f***ing psycho.
At the end of the film, White's feeling of responsibility for Orange's shooting morphs into a trust that Orange doesn't deserve. Joe's convinced Orange is the rat. White counters:
WHITE: Joe, Joe. I don't know what you think you know, but you're wrong.
JOE: Like hell I am.
WHITE: Joe, trust me on this. You've made a mistake. He's a good kid. I understand. You're hot. You're super f***ing pissed. We're all real emotional. But you're barking up the wrong tree. I know this man. He wouldn't do that
This trust in Orange's innocence is total, but it's White's undoing. He puts his life on the line for Orange. When Joe lifts his gun to shoot Orange, White pulls a gun on him and Eddie pulls his on White.
WHITE: Joe, you're making a terrible mistake. I'm not gonna let you make it.
PINK: Come on, guys. Nobody wants this. We're supposed to be f***ing professionals.
EDDIE: All right, look, it's been quite a long time, a lot of jobs. There's no need for this, man. Let's put our guns down and just settle this with a f***ing conversation.
WHITE: Joe, if you kill that man, you die next. I repeat: if you kill that man, you die next.
EDDIE: Larry, we have been friends, and you respect my dad and I respect you, but I will put f***ing bullets right through your heart. You put that f***ing gun down. Now.
Knowing what we know, this is a hugely dramatic and tragic moment. We're thinking, OMG, he doesn't know...
White goes down and even when he's mortally wounded, he crawls over to Orange and cradles his head. More OMG moments. When Orange finally admits he's a cop, White can't deal. He's sobbing, overwhelmed with anger and grief.
He shoves the gun in Orange's face and we have a few seconds to wonder whether he can bring himself to pull the trigger. With a boatload of cops with guns drawn ordering him to drop the weapon, he shoots Orange and gets blown out of the frame by gunfire.
Why this commitment to Orange? Sure he likes the kid, but he hardly knows him.
Maybe what White feels isn't trust but guilt—notice that he's the one who leads the shell-shocked Orange away from the dead Brown and dead cops. It's he who stops the car speeding towards them. White thinks, and even says to Pink,
WHITE: The bullet in his belly is my fault. Now, while that might not mean jack s*** to you, it means a hell of a lot to me.
White accuses Joe of not having any proof that Orange is a rat, but White himself has no proof that Orange is innocent. He lets his guilt feelings get in the way of his logic
What do we make of a cold-blooded lifelong criminal who manages to show compassion for a dying guy, and wants to get closer to his co-conspirators by revealing his name and other personal information? Who takes personal responsibility? He's a violent guy; he kills cops. Maybe not so cold-blooded? What gives?
Keitel told an interviewer that he never plays violent people; he plays conflicted people who have a need to use violence as a result of their conflict. That's the actor's take, though. Tarantino never gets into the psychology of his characters. He just shows us them being who they are and we try to figure them out.