John Proctor is prepared, albeit reluctantly, to confess that he's guilty of witchcraft. This is a completely false charge, of course, but under the circumstances, John feels he has no choice.
However, a merely verbal confession is not enough for Deputy Governor Danforth. He wants John to sign his name to a written confession that will then be nailed to a church door for everyone in Salem to see. Publicizing John's confession in this way will give it a much more official status.
The Puritans of Salem are people of the written word. Just as they venerate what's written in the Bible, they are very serious when it comes to written documents like property deeds and legal papers. The same applies to written confessions of guilt.
But John's not prepared to play ball. He knows his days are numbered, and although he may not have much left in life, he does at least still have his good name. If he were to sign a written confession, the Proctor name would be mud, not just for the foreseeable future but for generations to come. And as John's not prepared to leave his descendants with such a legacy of shame, he refuses to sign the confession.
Proctor feels compelled to retract his confession because he admits that people more innocent and closer to God are going to be hung. Particularly, Rebecca Nurse, who is an icon of virtue in the community. She is scheduled to die with Proctor.
Also, there is a practice that when someone confesses to witchcraft, their land is confiscated and sold at a discounted price. So if Proctor goes ahead with his confession, being pressured by Danforth and Parris to sign his name to a written confession to be hung on the church door, he will lose his property and soil his name, not only for him, but for his sons.
Proctor cries, "It is my name," he will only have one in his life, therefore, in order to bring dignity and honor to the Proctor name John must retract his confession. He can't bear the thought of living with a name that has been disrespected. Since he confessed to the adultery with Abigail, Proctor feels like he is right with God. He does not want to risk his immortal soul at this point. His wife, Elizabeth, agrees.
What's in a name? Everything. At least that is how it used to be. John Proctor has little issue with verbally saying that he is a witch, or even signing the document because a verbal statement is between him and his God. But when Judge Danforth wants to post it on the church door, Proctor won't stand for it. The difference between verbally saying something as opposed to putting it in writing is huge. By stating he is a witch, John Proctor feels that giving them this lie verbally, is in line with his view of himself as a sinner in the eyes of God and a fraud in the eyes of the ones he loves. However, posting his signed confession holds a deeper truth for John Proctor. He is not willing to shame his God, his boys, his wife, and even his friends. He will not allow his lie to ruin the reputation of his friends. The minute his signed confession is posted, he has ruined the names of his innocent friends. Also, the weight of posting his name upon his character is too much for him because he realizes that he is a good man, and he is not willing to throw away his "name" (reputation). His name is his reputation, and his reputation is his name. John Proctor states, “Because it is my name! . . . How may I live without my name? I have given you my soul; leave me my name!” Because he stands strong, John Proctor comes full circle in Miller's play and dies with the goodness that once defined him as a human being.
Proctor does sign the written confession, but he tears it up after he signs it. He tells the judges that they have witnessed him signing it and that is enough, but they want to post the signed document on the door of the church for all to see. Proctor says, they have his signature, but he wants them to leave him his name. He realizes that if this document that he signed, even though he knows the document to be false, is posted in public, his name will be ruined in the town. His children will grow up in shame and he does not want that to happen. The shame wouldn't be because Proctor confessed to knowing people who practiced witchcraft, but because Proctor lied. He only signed the document to save his children from growing up as orphans. Proctor tears up the document because he can't bear the lie that he perpetrated by signing the document. Arthur Miller is showing the audience what many who were persecuted, as supposed members of the Communist party, went through under the scrutiny of Sen. Joseph McCarthy and the others on his committee in the 1950's.