What is the significance of the frequent use of the name "Goody" in The Crucible?

"Goody" was a way to refer to married Puritan women. As Ulrich points out, "In seventeenth-century New England, women of ordinary status were called Goodwife, usually shortened to Goody."  The idea of "Goodwife" is significant.  Women in Puritan times were seen as extensions of the domestic realm.  Those who were married had to be referred to as "Goody" to reflect their capacity as a "Goodwife," as someone who embodies the qualities of the domestic realm.  It is for this reason that Goody Putnam, Goody Proctor, and Goody Nurse all are referred to as such.  They are married women and their primary function is to operate as a "Goodwife."  This condition of being in the Puritan world is what enables them to retain the "Goody" as part of their being.  

It is interesting to note how the term "Goody" preceded their names, almost to suggest that being a "Goodwife" took precedence over all.  There was no other construction of being for them.  In his stage directions preceding Act I, Miller suggests that part of the challenges that enabled the witch trials to gain so much traction in Salem was the narrow construction of being in the world.  Part of this involved the idea that there was no private life.  The idea of "Goody" was a public way of ensuring to the world that these women were good wives in the domestic realm, a predilection that Miller sees as distinctive of the time period:  "This predilection for minding other people’s business was time-honored among the people of Salem, and it undoubtedly created many of the suspicions which were to feed the coming madness."  The use of "Goody" was a way to show to the world that the women who were married were honorable "Goodwives." 

Why is the word "Goody" frequently used in The Crucible?

While Arthur Miller took poetic license with his characterization of Abigail Williams in raising her age and in creating her affair with John Proctor, he has established well in his drama the social setting and dynamics of the Puritans in Massachusetts. One of the elements of this realism is the prevalent use of the polite forms of Puritan address; namely, Goodman for men and Goody for women. So, Goody is used rather than the modern Miss or Mrs. or Ms.

Interesting, however, is the connotation attached to this word of address in light of the importance that the Puritan community places upon one's good name. Clearly, one's reputation is of paramount importance to those who people this drama, mainly because their religion is not a forgiving one that offers sacramental grace for confession as does that theology from which the Puritans broke. (Punishments for transgressions were severe and humiliating.) So, perhaps, the repetition of "Goody" may be a dramatic effect that Miller employs to remind the audience of the importance Puritans placed upon their good name. After all, in the end, John Proctor values his good name above all else. Indeed, it is his desire to preserve his name that leads him to tear apart his confession because it is not the same as what others say. Proctor feels he must retain his integrity:

Because it is my name! Because I cannot have another in my life! Because I lie and sign myself to lies! Because I am not worth the dust on the feet of them that hang! How may I live without my name? I have given you my soul; leave me my name!

Further he says,..."I do think I see some shred of goodness in John Proctor."