As you are quite likely to know already, many of the characters in those popular novels by J.K. Rowling observe a taboo against speaking the name of Lord Voltmeter. (This resonates with the special importance accorded to personal names in many real-life human societies as well as in many other fictional ones.) The characters typically work around this taboo by using kennings such as "You-Know-Who" or "Count Laszlo de Almásy." One of the most frequent of these circumlocutions is "He Who Must Not Be Named." This looks, at first glance, like a definite description,1 but, as it is used by Rowling and her characters, it has two properties characteristic of proper names.
The first and less interesting of these is that it is capitalized. This is primarily an orthographic fact, although when I hear the characters' voices in my head (which I do only when I'm actually reading the books, thank you very much for asking), the capital letters evoke a certain prosodic emphasis. It also doesn't necessarily mean very much, because Rowling also confers initial caps upon words such as hippogriff, which I would no more capitalize than I would the word horse.
The second, more interesting property of "He Who Must Not Be Named" is that it is invariant, as we can see in phrases such as "the downfall of He Who Must Not Be Named";2 if it were merely a description, rather than a name, we'd expect to see "the downfall of him who must not be named," with accusative case assigned to the pronoun by the preposition of.
I can't recall seeing a possessive version of this epithet, but given how it patterns in other contexts, you should in principle be able to say things like "He Who Must Not Be Named's wand." If it were a description rather than a name, we'd have our choice of three decidedly stilted alternatives: "the wand of him who must not be named" (portentious!), "his wand who must not be named" (extraposed, and potentially ambiguous), or "*his who must not be named wand" (ungrammatical).
At any rate, I find it amusing, in a quietly geeky sort of way, that all these wizards talking about "He Who Must Not Be Named" are, in fact, naming him. I guess it might be more accurate to call him "he whose real name must not be spoken," but then, that's not his name, is it? His name is "He Who Must Not Be Named."
1. The definition in the link suggests that a definite description must begin with the (and, at least as of a few minutes ago, the one on Wikipedia says so, too). But it makes sense to include pronouns (with or without relative clauses) here as well; after all, he, for example, means something like 'the guy.'
2. This is not a spoiler; it refers to an event that has taken place before the beginning of the first book in the heptalogy.