tolkiens legendarium - Do the bearers of the Elven rings know the identity of the other bearers?

I was just wondering if the identity of the owners of the Elven rings was known to the other bearers? In the Lord of the Rings, there is much mention of the identity of the wearers of the Elven rings needing to be kept secret (such as when Aragorn tells Frodo that he should not have spoken of Galadriel owning Nenya outside of Lothlorien), but I wonder if the owner of one of the rings could have hidden their identity from the other bearers?

Although it is a vague notion, the novel seems to imply that the 3 Elven rings are in some way linked. At the end of the novel I recall a passage describing Gandalf, Elrond and Galadriel all communicating with each other without actually speaking aloud - like some kind of telepathy. I think this is when they are travelling to the Grey Havens to leave Middle Earth so it lead me to wonder if this is down to the Elven rings, or some other reason.

Are there any references to these aspects in any other of Tolkien's works?

Answer

The mental communication between Galadriel, Elrond and Gandalf was most definitely not due to the Rings - their power was explicitly lost when the One was destroyed.

For the answer to that one we must look to the "Quendi and Eldar" essay published in the "War of the Jewels", section headed "Note on the language of the Valar":

For the Valar and Maiar could transmit and recieve thought directly

From there a CJRT footnote directs us to Annals of Aman paragraph 164, and from there his commentary references the RotK scene.

Gandalf/Olorin, as a Maia, is quite capable of recieving thought from the Elves and transmitting thought to them (this is touched on in Q&E in the paragraph following the quote I give), so even if the Elves can't do so between each other, Gandalf/Olorin certainly can facilitate it (much as a translator can facilitate communication between two people who don't speak a common language).

So much for the effect of the Rings here; back to the main question. This is answered in "Of the Rings of Power and the Third Age" (pulished in the Silmarillion) and I quote in full:

Therefore ere the Third Age was ended the Elves perceived that the Ring of Sapphire was with Elrond, in the fair valley of Rivendell, upon whose house the stars of heaven most brightly shone; whereas the Ring of Adamant was in the Land of Lorien where dwelt the Lady Galadriel. A queen she was of the woodland Elves, the wife of Celeborn of Doriath, yet she herself was of the Noldor and remembered the Day before days in Valinor, and she was the mightiest and fairest of all the Elves that remained in Middle-earth. But the Red Ring remained hidden until the end, and none save Elrond and Galadriel and Cirdan knew to whom it had been committed.

So, your answer is: "yes".