Who cares about their reputation in the crucible?
Correspondingly, what characters in the crucible are worried about their reputation?
Miller describes the importance of reputation through his characters, Reverend Parris, John Hale, Elizabeth Proctor, and Giles Corey. In The Crucible, some characters will do anything to protect their reputation and others do not seem to worry. One character that lives and dies around his reputation is Reverend Parris.
In this manner, why does Reverend Parris care about his reputation?
The Reverend Samuel Parris is very concerned about his "name." By that, we mean that he is very worried about his reputation -- the way people think of him. This is partly because he is the town's minister. In Puritan times, this was a very important position and he would have felt the need to have everyone trust him.
A person's 'name' was equivalent to their reputation and how they were known by everybody. Having a good name had become especially important in the town of Salem, due to the witchcraft trials, where the untrue accusations made in court could easily end a person's life.