From Wikipedia:

There are several explanations for the origin of the style, "William the Silent" (Dutch: Willem de Zwijger). The most common one relates to his prudence in regard to a conversation with the king of France.

One day, during a stag-hunt in the Bois de Vincennes, Henry, finding himself alone with the Prince, began to speak of the great number of Protestant sectaries who, during the late war, had increased so much in his kingdom to his great sorrow. His conscience, said the King, would not be easy nor his realm secure until he could see it purged of the "accursed vermin," who would one day overthrow his government, under the cover of religion, if they were allowed to get the upper hand. This was the more to be feared since some of the chief men in the kingdom, and even some princes of the blood, were on their side. But he hoped by the grace of God and the good understanding that he had with his new son, the King of Spain, that he would soon get the better of them. The King talked on thus to Orange in the full conviction that he was aware of the secret agreement recently made with the Duke of Alba for the extirpation of heresy. But the Prince, subtle and adroit as he was, answered the good King in such a way as to leave him still under the impression that he, the Prince, knew all about the scheme proposed by Alba; and on this understanding the King revealed all the details of the plan which had been arranged between the King of Spain and himself for the rooting out and rigorous punishment of the heretics, from the lowest to the highest rank, and in this service the Spanish troops were to be mainly employed.[27]

Exactly when and by whom the nickname "the Silent" (Modern Dutch: "de Zwijger", meaning more "the Taciturn". The verbs "zwijgen" in Dutch, "schweigen" in German, "tiga" in Swedish, "se taire" in French, "callar/callarse" in Spanish and "tacere" in Italian have no real equivalent in English; they mean the opposite of "to talk".) was used for the first time is not known with certainty. It is traditionally ascribed to Cardinal de Granvelle, who is said to have referred to William as "the silent one" sometime during the troubles of 1567. Both the nickname and the accompanying anecdote are first found in a historical source from the early 17th century.[28]

In the Netherlands, William is known as the Vader des Vaderlands, "Father of the Fatherland", and the Dutch national anthem, the Wilhelmus,[29] was written in his honour.