Q:

Was the Silence Prophecy fulfilled in The Name of the Doctor? 

On the fields of Trenzalore, at the fall of the Eleventh, when no
living creature may speak falsely or fail to give answer, a question
will be asked.  A question that must never, ever be answered. 
Doctor Who? 

In The Name of the Doctor the Doctor and Clara went to Trenzalore and it was revealed to be his grave.   Was this the fulfilment of the prophecy which the Silence wanted to avoid? 

On the fields of Trenzalore

Although I wouldn't describe it as a field - Check

at the fall of the Eleventh

Well, the Doctor didn't die - we also weren't given a reason to believe he wouldn't have any more regenerations.   So was this where the 11th will fall?   He did technically fall to the ground?  You could also say he was defeated... Unsure

when no living creature may speak falsely or fail to give answer

But he did fail to answer - sure River answered but he didn't?   However there was the spoiler at the end which implied River was with the Doctor, did she answer for him?   Again, unsure. 

a question will be asked.  A question that must never, ever be answered

Now, this is the kicker.   The Doctor's name was asked, however I suspect the question is actually slightly different... who was the "Doctor" we saw at the end? 
The final point is idle speculation as we can't know until the the writers reveal it.   However my question is this, was this the the fulfilment of the prophecy or are they going back to Trenzalore at some point in the future (before he dies)? 

A:

I don't believe so.   It sounds to me like the prophecy is about the battle that resulted in the graveyard we see in The Name of the Doctor.   During that battle, Silence fell.   The main reason I think this is the case, is because:

when no living creature may speak falsely or fail to give answer

wasn't really part of the events of that episode.   The Doctor clearly failed to give an answer, River was the one who provided the answer. 

We see the events of the prophesy play out in the recent Christmas Special episode, The Time of the Doctor.   In it, The Doctor and Clara go to a world revealed to be Trenzalore.   The crack from Series 5 is in a building on the planet, in a small town.   It is emanating a 'truth field', which prevents people from 'speaking falsely' (see above prophecy).   A signal is coming from the crack, which contains an encrypted message asking a question over and over:

Doctor Who?  

They come to the planet, and find many ships from various races.   Each race sent one ship to investigate the signal, which is being transmitted throughout time and space.   The Church got there first.   To protect the planet, they setup a shield to prevent anyone from going to the planet or attacking it.   When the Doctor arrived, The Church sent him down to investigate. 
The signal is coming from Gallifrey, outside the universe after the events of Day of the Doctor.   If the Doctor speaks his name they'll return, but in so doing, will restart the Time War.   Upon learning this, The Church dedicates themselves to Silence, the silence of the Doctor, as they do not want the Time War to return.   As The Church's leader proclaims:

Silence must fall. 

A repeating theme of the 11th Doctor's run, and something related to the prophecy, "Silence will fall when the Question is asked" (Let's Kill Hitler). 
So The Church helps maintain a truce, they help the Doctor prevent any of the races from invading the planet, and he does not answer the question.   Then time passes as they maintain the truce.   Centuries pass, the Doctor grows old. 
At the end of the episode, the Daleks break the truce and invade the planet.   Clara argues into the crack that the Time Lords don't need to hear the Doctor's true name, they just need to help him.   They do so by providing him with a new set of regenerations.   The 11th Doctor dies of old age, blasting the Daleks with his regeneration energy, saving the planet as his regeneration begins. 
And so the Eleventh falls.