What does John's name symbolize in The Crucible?

The name John in Hebrew means God is gracious. The name Proctor means steward, or charged with the care of something.

In The Crucible, John Proctor embodies the fullness of the promise of God's graciousness and forgiveness.  He is a sinner, one who has repented and asked for God's mercy.  So at the end of the play, when he decides to die valiantly to save his immortal soul, he is putting himself into God's gracious hands.

His name, as well as his execution are symbolic, it is after his death that the witch trial hysteria ends.  He is the representative or steward seeking God's mercy and graciousness for all sinners.  Proctor shows how God's forgiveness, even in the presence of great sin, can save one's soul.  Proctor, God's emissary, bravely surrenders his life, restoring the dignity to his name, removing the shame and guilt from his sin, cleansing it for his family, his wife and children.

The false accusations against a man like John Proctor have such enormous implications that Reverend Parris knew that his confession nailed to the church door would carry great weight in support of the legitimacy of the court's rulings on witchcraft in Salem, instead, in dying for his faith, John Proctor becomes a Martyr.   

A symbol for the injustice of the witch trial hysteria.  Proctor's death proves the illegitimacy of the court's authority, the exact opposite of what the court, Danforth and Parris hoped to achieve.