The character in The Crucible is John Hathorne. John was the great-great-grandfather of Nathaniel Hawthorne. Hawthorne tried to distance himself from his great-great-grandfather and his family history, which may have led to his name change.
Nathaniel Hawthorne had three children. They were: Una Hawthorne, Julian Hawthorne and Rose Hawthorne. Their first was their daughter, Una, who was born March 3, 1844. On June 22, 1846, their second child was born, his name was Julian. Their final child, Rose, was born in May 1851. - wikipedia
Nathaniel Hawthorne, or originally known as Nathaniel Hawthorne. He changed his name to disassociate himself from his relative John Hawthorne, who was a Salem witch trail judge at the time. This just showed his contempt for a portion of the 'puritan' method.