I applied for some research positions and send the name of my references. I would like to know that: Do the full list of my references will be forwarded to each of professors by institute which I applied for. In other words, Will professors whom I add their names as my references be informed about the name of other references of mine?
While anything is possible, I think that would not be normal practice. I think it is unlikely.
However, in some smaller fields in which there are fewer professors and they know one another, it is possible that someone will mention a name to another person. But this would only occur, I think, if there was some question raised by a letter of recommendation.
Normally the process of solliciting and receiving reference letters is confidential: it implicitly discourages the possibility of two referees somehow harmonizing their references to the advantage or disadvantage of a candidate.
Of course people talk and people use their common sense: it’s likely that a member of supervisory committee will have guessed that other members of the committee will also serve as referees. It’s also possible that a candidate might let a prospective referee know who the other referees are so as to provide context.
Most reasonable people will write a reference letter to reflect their personal appreciation of a candidate; while general statements can be shared between colleagues and some specific phraseology can be discussed, I have never shown a final version of a reference letter to a colleague, and no colleague of mine has ever shown a final reference letter to me.
However, it would be very unusual for an institution to solicit a letter of support and announce the list of referees for a candidate.