Elijah Millgram wrote an interesting essay for a volume on Nozick (called Robert Nozick) about philosophical persona-construction as an alternative to philosophical theory-construction, titled "How to Make Something of Yourself" (say what else you will about him, the guy at least has decent titles—the last thing I read of his was "On Being Bored out of Your Mind"), in which he identifies various members of the tradition, including Socrates, Nietzsche, Kierkegaard, Montaigne, "probably, the later Wittgenstein", maybe Foucault and Nehamas (he has his doubts), and Stanley Cavell (p 175). He claims that Nozick's The Examined Life "is an exercise in this genre as well" though doesn't say whether he takes Nozick to belong tout court. He also says that Oscar Wilde is not a representative (178), a claim which he qualifies by noting Wilde's "criterion for being a successful work of art, which invokes the secondary qualities it makes perceptually available" (I take it this is taken from the dialogue "The Critic as Artist"), but says "the characterization stands … he himself was neither philosophically trained nor interested in philosophical questions" (195n14).
I'm not so sure about the reasoning here (about the classification I'll keep to myself). Nozick frames EL as something of a portrait which is part of his own life (ie not a representation at a particular stage), and notes that the material of portraiture used to create the persona will be "made up of theoretical pieces" (Millgram quotes this on 179), leading Millgram to pose the question of why it is that so often exercises in philosophical persona construction take the form of an orientation toward theories, as if they were philosophically primary. He considers Nehamas' answer to the question, that if one weren't oriented to theorizing, one simply wouldn't count as a philosophical persona, and convicts it on two grounds: first, it's merely taxonomical (I'm not sure why this is supposed to be a strike against it, but that's how he presents it); second, it makes theory primary and personae derivative, when, at least in ancient times, it was the other way 'round, and, furthermore, this makes the point of the persona obscure. So Millgram's counterproposal: the reason theorizing (in some form) so often shows up in such personae is that "the activity of theorizing is a component of the well-lived life" (180, italics in original), and, of course, since we are dealing with personae meant to display lives of some such sort, theorizing is going to play a role in them.
But look at what Millgram considers when talking of orientation towards theory: it takes the form of an explicit orientation. His examples are Socrates demanding theories of others, or in unnamed but more common cases, treatments of earlier theories (179). But there's also an orientation towards theory which is: "no theorizing!" To abandon philosophy to be a rural schoolteacher, or an auto mechanic, or to have philosophical ideas and a familiarity with the somewhat recent philosophy of one's time (as Wilde certainly did, training though he may have lacked; IIRC there are references at least as far back as to Kant in some of his dialogues, though I may, after all, recall incorrectly) but to show no particular concern with working a consistent theory into one's own life, would not be to construct a philosophical persona.
I actually agree with that, I think, at least as far as the schoolteacher (though this case is complicated) and auto mechanic examples go; as I said I'm not so sure about Wilde. But I don't at all agree with Millgram as to why. I also don't think that someone who left the worldly world to join a monastery, even if to contemplate the true order of the world, or whatever, would have a philosophical persona. But this is because philosophy, despite the name, isn't, at least as it's practiced nowadays, actually about the love of truth. Contemplating the eternal won't suffice. Love of truth, yes, but love of truth-spreading much more. Hence argument, the theoretical tradition: a good way to convince others, and to sharpen your own grasp. Hence, if you've got a persona, it had better be notorious.
(This is why the schoolteacher case isn't so clear, and why it surprised me, initially, to see only the later Wittgenstein on Millgram's list. Wittgenstein already had quite a lot of notoriety and fame as a philosopher when he went off to teach preteens, and as far as I understand things it was a philosophically motivated decision. "Schoolteacher" isn't much of a persona, but to abandon philosophy for humbler work (after teaching, he worked as a gardener's assistant), especially considered in light of what is I suppose an unsophisticaed reading of some of the comments about the self in the Tractatus, seems a rather philosophical decision itself, and if he could have kept it up, he could have shown something thereby. Along possibly related lines consider GCL, "Ist denn etwa die Lage so selten in der einem Philosophie das Philosophieren versagt?" (J1234, quoted in German and not English because if I go through the trouble of finding the damn thing, you can be damn sure I'm going to quote it). That demand on being public—because, as Millgram notes, you're supposed to be interested in convincing others, logically (hopefully!) or psychologically (less admirable!), and you can only do that if, you know, the other is aware of you—will in Lichtenbergian cases kind of bite you on the ass, if you've got the truth-spreading conception of philosophy: philosophy denies philosophy to you, but philosophy does so, so you'd better make a big deal about how you're leaving philosophy philosophically, but then you've undermined yourself … oy veh.)
It's not seeing that demand on actually being publicly available that leads Millgram to make some kind of odd claims. He makes the following claim: "that the most visible philosophers of the personal tradition are, almost uniformly, very hard to take … many of the mare positively—to use an ordinary but vivid word—creepy" (p 181, italics in original). I won't comment on that except to say that it seems kind of churlish to say that when Cavell is still alive (and is he creepier than, say, Kripke?) after singling him out as a "well-known contemporary representative" (175). It's the explanation for this claim that seems to get things a little backwards. First: "it is natural, when going into the business of fabricating a persona, to be ambitious about it … Especially when one identifies oneself with one's persona, one wants to do one's very best" (184). But if you've got an elaborate persona, you've got two problems. First, it'll be hard to keep up. (That seems nonobvious to me. You might take to it like a sheep to slaughter, no?) Second, it'll be hard to keep to the plan. (Same question, I guess.) But one can solve both those problems by one and the same means: make the persona psychologically compelling—fascinating is Millgram's apt word (apt because. I think many people don't know this). Then, you yourself will also be compelled, and you'll attract a bunch of sycophants who'll keep you on the straight and narrow.
This doesn't, according to Millgram, happen to every exponent of the persona-creating tradition; in particular, it doesn't happen to Nozick, and the reason is that in The Examined Life he affirms so few positions that he can wander around and consistency isn't a big worry. (Millgram suggests that something similar's up with Montaigne.) One result of this is that it isn't actually fascinating or compelling at all, though. Even when it does happen, though, I would be very surprised if it has the etiology Millgram describes. Take the bit I quoted from him about "going into the business of fabricating a persona". A mite uncharitable: but perhaps some of the philosophers in the tradition do decide to create personae "ambitiously". It seems more likely that some people decide to create outsize personae as such, but philosophers have certain beliefs that lead them to have outsize personae, or at least to feel constrained to certain narrow possibilities (as in, eg, Beyond Good and Evil 213 or Gay Science 290), without having "gone into the business", as if they could have just as well wound up with quite humdrum personae but for their untamed lust for, what, eccentricity?
But the reason for the persona to be compelling is not that that way, the person personating will be motivated to keep it up, or to attract followers to keep that person in line; it's that, if you think that philosophy is about communicating something, you're going to have to make yourself bright and colorful enough to attract notice. Nozick says (Millgram quotes on 179) that the personae's "lives play a crucial role in convincing us of what they say … If we accept their views upon their authority … that authority is derived only from what they are and show in their lives". And at the end of his essay (192–3) Millgram considers various ways showing a life might be compelling logically, and not just fascinating. If the ability to do that kind of thing is your criterion for even being philosophical, then you'll only count as adequate philosophical personae those that attract a certain amount of attention. There are various reasons you might attract attention: you could already be famous as a philosopher, like Wittgenstein or Nozick himself. You could gain fame as a writer, as Montaigne did, even if during one's own life one was not primarily known as a writer. (Lichtenberg might be another example of this, all the more interesting in that the waste books were always private and only published posthumously—he clearly wasn't developing what personality comes through there in order to compel by any means, no one ever being intended to read them.) Or, you could just have a really notable, unusual persona in life. But if you had an outwardly ordinary persona, or even just an outwardly not extremely distinctive persona, you would be disbarred beforehand from being part of the philosophical persona tradition—so of course when you take a count of the tradition, you'll find a larger than usual number of fascinating gurus with no-account epigones. You'll also find that many of them have, in some way, explicitly to do with theories and theorizing.
If, though, you have a conception of philosophy on which convincing others or spreading the truth is less central, or if you allow that an engagement with theory or philosophy itself can take the form of disengaging and still be properly philosophical, then it's possible that there's any number of philosophical personae out there of which one simply knows or suspects nothing, because it would be the mark of that kind of persona that it doesn't necessarily seek to make itself philosophically notorious, or engage in actual courses of theoretical (or, for that matter, written) disputation.