Proverbs 22:1 says, "A good name is rather to be chosen than great riches, and loving favour rather than silver and gold." Considering that Solomon, who had incredible riches, was the one who said this, having a good name must be very valuable.
There are two reasons why we should strive to have a good name. First, we need a good name so we can serve God well. Consider this- a person can spend a lifetime building a good reputation, only to tear that reputation down in a few short minutes of folly and sin. And while God definitely forgives sin, men aren't quick to forget. For example, a pastor could live his whole life in a Godly way, but even one moment of yielding to temptation could totally destroy his ministry. Why is that? It is because people would have a hard time trusting him again.
The second reason we should have a good testimony is this- as Christians, we don't want to give unbelievers an occasion to blaspheme God ( 2 Samuel 12:14 ). When we don't walk what we talk, the world looks at us and says, "I definitely don't want to be like THAT hypocrite!" When we act ungodly, we are being a terrible witness.
So remember- as Christians, we are to be Christ-like. If someone could see you every minute of every day, would they think that you were more like a little Christ, or a little devil?