[Ibrîniðilpathânezel]

One has to wonder if the name 'Imladris' was even known to Denethor. He doesn't appear to have any interest in anything that does not directly concern Gondor. If he somehow perceived Elrond and his realm to be of potential benefit to him, he would certainly have known the name (if not where it was located), but he had a demonstrated tendency to dismiss any knowledge that he could not see being of use to him (witness his reaction to Gandalf's research in the archives of Minas Tirith). If he knew the word, he would have known that the realm was hidden, and thus of little use to him -- until his sons had a dream involving it, one that seemed forbidding and prophetic, for Gondor. Suddenly the place has meaning for him, but there is no one to ask about its location, and no time to waste in potentially futile research.