Danny handed his friend the controller, feeling a bit of triumph at his high score. Even the principal, who thought videogames were the tools of the devil, would be impressed if Danny won the big videogame match. But he had to beat Tyler here first!
Well, you know me and rules. Tools, not rules! Deep POV is not a set of rules, but a mindset that allows the writer to write from within the character, in the character's own voice. But... but you're still writing. That is, no matter how closely you try to replicate the character's inside experience, you're doing this with words. And therein lies the issue.
Okay, here's my question. If you ignore any supposed rules about what deep POV is supposed to require, and concentrate just what I said, drawing the reader into the experience of being that character, what do you think works?
See, the character Danny knows who he himself is. When he's thinking of himself, he doesn't have to use his name because, well, he doesn't think "he" is anyone but himself. To the extent that he thinks in language at all, rather than just has consciousness of "me vs. other," he'd think "I", right? He wouldn't even think "he".
But the reader isn't him, and this isn't first-person. So already you're imposing a different experience on the reader, and it doesn't help much to say, "Well, he wouldn't think of himself by name," because he wouldn't think of himself as "he" either. He wouldn't think, "I'm not
The reader already is making an allowance-- has to make an allowance-- for certain conventions of narrative, and the first is... this is all done in words, when, in fact, experience has very little to do with words. We have only language to convey everything in the world of the book-- how the snow sounds when you walk on it, and how the moonlight glints off her hair, and what it feels like to realize your lover is cheating on you. That's it-- but we really can convey it all in words, enough so that for several thousand years, written language (and spoken language for much longer) has been the dominant way of conveying and recording experience. Right? Right.
Okay. Given all that-- given that we convey experience using words, how do we convey what it's like to be Danny? Well, the first thing is acknowledge that "Danny" is who he is. That name is a construct, of course, but it's a construct that conveys everything about who he is. Everything that is Danny is symbolized by the name Danny. When one of his friends tells the tale of how they almost got arrested but Danny got them out of it, he says, "But that's Danny. Silver-tongued. He could talk the devil into converting to Catholicism." When Danny tells his mother that he's working 20 hours a day, she sighs, "Oh, Danny, you're just like your granddaddy, and he died of a massive heart attack when he was 40."
That is, Danny IS Danny. The reader knows him as Danny. If we're lucky, the reader can even, for a short time, BE Danny. But Danny is Danny, and there's no shame in that. Use the name. Of course. "Danny" is at least as much of who he is than "he" is. In fact, I bet he thinks of himself as Danny a lot more than he thinks of himself as "he"-- "Well, Danny, my boy, you've really gone and cocked it up this time."
Now given that this is third person, so there's not that easy distinction of first person ("I" and "everyone else"), and that the reader expects a certain level of narrative conventionality (that this is all in language, that it's in past tense even though to Danny it's happening right now, that Danny has to think of himself as "he"), the question is: What will give the reader the experience you want?
What will let the reader "sit in" the character?
What brings the reader out of the character first thing, immediately, automatically, is confusion. As soon as the reader has one jot of confusion that the character doesn't feel, one moment of not knowing what the narrator means, that's it. There goes the deep identification. "I'm not that person! I'm me, the reader, and I don't know what the heck is going on!" It takes only a second, and you've interfered with the reader's deep identification with the character.
What confuses the reader? Well, Danny knows who he is. He knows his achievement is something the principal would disapprove. He knows he feels a moment's triumph. He knows he got a high score. See what I mean? You have him think that "out loud," in words, though of course he already knows that. There's no other way to let the reader in on his thoughts and knowledge than to just say it in words.
Now why is only one word in all the world -- his name-- barred from use in conveying what Danny knows?
It's a fake rule, frankly. It's illogical that everything else-- the whole world, his whole consciousness, his whole being-- is conveyed in words, but you can't convey, "This is Danny, and this is the other guy," in the simple shorthand way of USING THEIR NAMES?
You can. When they invent some USB cable that truly lets us be inside another person's experience, maybe we won't need words. But we do. And we're writers, and we should love words. :)
Anyway, the worst danger in deep POV is to eject the reader from the experience. Trust me here-- the reader will NOT be ejected by the mere sight of Danny's name. She won't think, "Wait a minute! Danny called himself Danny, and that means-- while him calling himself 'he' didn't-- that I am not him!! Oh, my gosh! I'm not named Danny! I'm not even a man! I'm not living in the Cotswalds! I'm out of here!" The reader won't even notice. (You can, of course, do it maladroitly enough that the reader notices, like use the name 24 times in 24 lines, yes, but you're not doing that. :)
But what WILL eject the reader from the experience is confusion. If the reader for one second doesn't know what's going on (and the character presumably does), then the bond is broken. So it's much, much, much more important to create a smooth identification experience, a protected space of connection, a cocoon of consciousness, where the reader can trustingly BE, and BE IN the character.
So-- long long answer. Yes, use the name when the reader needs it. Why not? It's far more important that there is no "bump" of "huh? Who is that?" that reminds her, as "Which he is this?" will do, that she is not he.
This is hard. Don't make it harder by denying yourself the character's name. We need more words, not fewer, to help us create this fictive experience for the reader.
Sorry to go on so long, but "you can't use his name" is #1 Deep POV Myth. :)