Granted, if I was an immortal, nigh-invincible undead monster that only gets more powerful over time, I probably wouldn't opt for a title that declares my one weakness.

This is only really a problem for D&D Liches, that have the phylactery thing, but I'm just saying - if I were one of them, I'd be spreading a title like "Xefas, He That Is Easily Maimed With Nonmagical Swords", or "Xefas, Pope of The Electrically Conductive", or even just something neutral, like "Xefas, Emperor of Funkytown".

I wouldn't say "Xefas, The Lich King", because now everyone knows I'm a Lich, rather than assuming I'm one of the other billion kinds of undead. Hell, you're better off magically disguising yourself as a demon, or a fey, or something, and being Xefas, Demon Prince, or Xefas, Princess of Fairybunnies - something to make your inevitable competition bring the wrong kind of kryptonite.