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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?