According to the wiktionary, a "name" is "any nounal word or phrase which indicates a particular person, place, class, or thing." Implications:
- "The Dark Lord" is a fully valid name.
- There is no reason whatsoever why a character should not have more than one name. As a matter of fact he can have as many names as intelligent entities who are referring to him or her.
- I don't think multiple names can be ranked. They refer to the same thing, and there is no reason why one should be better or more powerful than the other.
Additionally, recall that a number of languages have rather "telling" names. Indian and Turkish names, to my knowledge, can usually by literally translated, for example into phrases like "The one with the skin like moonlight", the same goes for a number of Gaelic names and so on. These names are in league with the likes of "The Dark Lord", we just don't understand it because we don't speak the language.
My point is: We name things. All the time. I'm not even sure our brains can process thought about things that we haven't previously named, even if that name is horribly clumsy such as "that weird wiggly thing on the other side of the road".
tl;dr: You do name your character. It just so happens that your name is not a canonical first name such as John or Mary. However, in my opinion, that is not a problem. Consider Moby Dick. The first line of this book is "Call me Ishmael", indicating that his real name is something else. Yet, to my knowledge, nobody has ever complained about this.