"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."