Abigail Williams is an original character created by Miller in The Crucible, but she is based on a real historical figure, Anne Putnam.
"The Salem Witch Trials took place in Salem, Massachusetts in 1692, and were based on the accusations of a twelve-year-old girl named Anne Putnam" ("The Crucible: Introduction").
Like Anne Putnam, Abigail Williams' character is twelve years old and grows up in a Puritan community in Salem, Massachusetts. Most likely, Arthur Miller changes Anne's name to Abigail Williams for artistic license. He wants to use the idea of the Salem Witch Trials as the backdrop for The Crucible without feeling tied to the necessity of maintaining complete historical accuracy. His characters and motives are his own original creation, defined by the events, culture, and values of Puritan New England in the late seventeenth century.