Unless Mokuran is incapable of thinking herself, Ebon's telepathy only picks up surface level thoughts. He can't go rooting around for memories. But he can tell how your mind is somewhat working, discerning mood, motives, internal monologues, and focus. If he asks you what your name was, even if you don't tell him he should be able to pick it up if you think your name for even a moment. I liken his power sort of like Nodoka from Negima, though he doesn't need a book or multiple artifacts.
Everything that Mokuren hears inspires a branch of sub-thoughts, that could range from the Pride of the Cheese-Men to how that sounds like someone getting cut in half with a very sharp sword. There is a chance one of those thoughts might relate to the topic at hand, but there would be several other thoughts at the same time. Mokuren herself has managed to distance herself so it is simply a mildly irritating buzzing noise, but reading her mind, even suface thoughts, could be jarring.