Advantages & Disadvantages of have Anonymous Retrospective.

I think this area needs some filling in regarding my scrum education. What is anonymous retrospective exactly, and how does it work?

Scrum has nothing to say about whether or not the Sprint Retrospective should be anonymous. What is missing for me in the question is why the Scrum Team wants this event to be anonymous. Might this be covering up other issues?

In most cases, there are few advantages if any - a loss of collaboration, transparency, and consensus building will be difficult if at all possible if Scrum Team members can't get together in a Scrum event.

I agree with @Chris. I had a team once that wanted to have anonymous retrospectives.  It caused more problems than added benefit.  For one, because everyone tried to be anonymous, the topics of discussion suggested were extremely vague. And when someone asked for clarification, no one would provide any because it would do away with the anonymity. We tried it 3 times and then the team finally spoke up and said "this sucks".  We never tried it again.

The point of the retrospective is so that everyone can openly discuss topics and come together for suggested changes or opportunities. I have found it helpful to share the "Prime Directive" for retrospectives with teams when they start up or have difficulties with the Retrospective. I honestly do not know the origin of this but have found it useful.

Regardless of what we discover, we understand and truly believe that everyone did the best job they could, given what they knew at the time, their skills and abilities, the resources available, and the situation at hand.

What are the Advantages & Disadvantages of have Anonymous Retrospective.

If team members are unable to collaborate freely and openly with each other in a Sprint Retrospective, what are the chances of them doing so during the Sprint itself?

I suggest reviewing the Scrum Values with the team, especially "Openness".

Per Scrum Guide: "The Scrum Team and its stakeholders are open about the work and the challenges"

The purpose of going anonymous matters the most. 

Is it killing the trust and openness? Then it is anti scrum