I think that we can safely speculate that, given the negative connotation that is really clear by the tone of the sentence, it is a name given to an enemy. The most probable options, in my opinion, are:
This is the most probable option; The Tolkien Gateway reports that amongst his names there is a pretty similar Nameless Enemy (The Encyclopedia of Arda does not list his names).
Furthermore, form the passage that you quote, we know that the people speaking are the men guarding the walls of Minas Tirith; it is implied that the interlocutors know who this Nameless One is without the need to explain further, a sign that it is a know and established thing amongst them. They were soldiers, not scholars or savants, so it is safe to assume that this great enemy that they are afraid even to pronounce the name is the one that is the closest to them, that is Sauron.
Another less plausible option is that they are referring to the arch-enemy of the whole Arda, a name that could be fearful in itself even if not the most immediate threat. Neither The Tolkien Gateway nor The Encyclopedia of Arda explicitly report this name referred to Morgoth, but we can assume that if Sauron was feared to the point of being scared to speak aloud his name, even his former Master could be rightfully considered at least equally terrifying.
The reason why speaking out loud the name of an Evil (Demi)God was considered a bad thing is that in a magical world like Arda, Words are not just part of the language, but they have a magical connotation, in a sense they act as spells themselves1.
Explicitly pronouncing the name of the powerful enemy that you are fighting was something that the people of Gondor aren't eager to do: in a certain sense is like summoning him, invoking his name.
Even in the real world mythologies, the true name of a God is a powerful Word, one that if pronounced can give you control over Him and His creations. The concept is similar.
Or you might even consider a superstitious concept that we have here in Italy (I'm not really sure how much this thing is international), called Scaramanzia, that basically means that there are certain words, phrases and gestures that can inherently cause good or bad luck, like if you say a certain thing, that thing is not going to happen; in example, if you say "I'm certain that today I would have a great day", you are scaring away all your luck and you will end in having a terrible one.
1 - As an example, you can read about the power of the name Elbereth in this article, or you can find a more general and detailed analysis about the whole subject from an essay by Stephanie Ricker, called The Power and Purpose of Names and Naming in Tolkien's The Children of Hurin (direct link to PDF).