Reputation is the result of CHARACTER.

“If I take care of my character, my reputation will take care of itself.” 
- Dwight L. Moody

This is an excellent quote on its own merit, but after reading the biography of Moody's life, knowing how often and harshly he was criticized by people, especially believers, this statement is quite profound. He was not impervious to the sting of slander, as he had a heart that felt deeply like any human, yet he did not buckle under the onslaught of arrows aimed at his back. He was a living example of Proverbs 26:2. Like a fluttering sparrow or a darting swallow, an undeserved curse does not come to rest.
People may not have liked his manner or his methods, but he was not living for the praises of men. Moody had one goal: To save sinners from the grip of hell. Always, with tears.
And he did so faithfully, day after day until the Lord called him HOME.

“If I take care of my character, my reputation will take care of itself.” 
An excellent perspective that begs the question - How do we take care of our character?
As always, there is only one place to find the answer. Scripture.

Finally, brothers, whatever is true, whatever is honorable, whatever is just, whatever is pure, whatever is lovely, whatever is commendable, if there is any excellence, 
if there is anything worthy of praise, think about these things. Philippians 4:8

For this very reason, make every effort to supplement your faith with virtue, and virtue with knowledge, and knowledge with self-control, and self-control with steadfastness, and steadfastness with godliness, and godliness with brotherly affection, and brotherly affection with love.
II Peter 1:5-7

Put on then, as God's chosen ones, holy and beloved, compassionate hearts, kindness, humility, meekness, and patience, bearing with one another and, if one has a complaint against another, forgiving each other; as the Lord has forgiven you, so you also must forgive. And above all these put on love, which binds everything together in perfect harmony. And let the peace of Christ rule in your hearts, to which indeed you were called in one body. And be thankful. Colossians 3:12-15

I appeal to you, therefore, brothers, by the mercies of God, to present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship. Do not be conformed to this world, but be transformed by the renewal of your mind, that by testing you may discern what is the will of God, what is good and acceptable and perfect. Romans 12:1-2

If we are faithful to obey these commands, we can build solid characters of godliness, and thereby possess reputations respected by others, and more importantly, reputations that please God. 
Only let your manner of life be worthy of the gospel of Christ, so that whether I come and see you or am absent, I may hear of you that you are standing firm in one spirit, with one mind striving side by side for the faith of the gospel, ... Philippians 1:27

Notice, the verse calls us to lives worthy of the Gospel, not lives worthy of self, or the approval of man. As Moody's life shows, no matter how faithfully and passionately we pursue God, everyone will not like us, approve of us, or want us. We cannot control what others think of us or how they perceive our words and actions. The only thing we can control is how often we meet the Lord in prayer and the study of His Word, and let Him take care of the details.

Criticism can cut you, shake you, and knock you off balance, 
but no criticism ever gets the final word over your life.
God gets the final word in Christ. 
- John Piper