According to the Watchtower Society, the word "Reproach" is defined as follows:

Defamation, disgrace, or scorn, whether for just cause or not. Commonly translated from the Greek noun o-nei-di-smos′ (and o′nei-dos) and the Hebrew noun cher-pah′(Insight On the Scriptures, 1988, Vol.2, p.779).

The Watchtower Society teaches that it is a very serious action to bring reproach upon Jehovah's Name. The members are continuously reminded to beware that their conduct does not bring reproach upon Jehovah:

One of the qualifications for an overseer in the Christian congregation is that he “have a fine testimony from people on the outside, in order that he might not fall into reproach.” This would prevent bringing dishonor to the position and would avoid the spread of unfavorable talk about true Christians because of the conduct of one of the prominent members of the congregation (Insight On the Scriptures, 1988, Vol.2, p. 780).

Indeed, our clean appearance and fine conduct will bring glory to, not reproach on, Jehovah and his holy name. (Keep Yourselves in God's Love, 2008, p.87, para. 2)

The Watchtower Society also teaches the Jehovah's Witness members that they should do all they can to avoid bringing reproach upon Jehovah's Name:

If we deeply desire that Jehovah’s name be sanctified, or held sacred, we will strive to avoid doing anything that would bring reproach upon it. (The Watchtower, December 15, 2007, p. 12, para.9)

Jehovah's Witnesses are taught to be extremely wary of performing any conduct that could be viewed as reproach upon Jehovah's Name:

Your love for Jehovah will move you to avoid committing a serious sin that would bring reproach upon his name... (The Watchtower, November 16, 2006, p.21, para.5)

True Christians, therefore, endeavor to maintain fine conduct in order to avoid bringing reproach upon Jehovah’s name.(The Watchtower, May 1, 2001, p.19).

Without a doubt Jesus was concerned about the charge of blasphemy that he saw would be hurled against him, the worst crime a Jew could possibly be guilty of. Why be concerned about a false charge? Because his death under that circumstance would bring reproach upon his heavenly Father. Yes, the spotless Son of God, who so loved righteousness and hated lawlessness and who had come to earth to glorify his Father’s name, was now to be put to death by God’s own people as a blasphemer of Jehovah God (The Watchtower, February 15, 1987, p.13, para.16).

Poverty has brought trial and temptation to many... , a Bible writer makes this helpful petition: “Give me neither poverty nor riches. Let me devour the food prescribed for me, that I may not become satisfied and I actually deny you and say: ‘Who is Jehovah?’ and that I may not come to poverty and I actually steal and assail the name of my God.” (Proverbs 30:8, 9) This prayer has helped many true Christians to remain trustworthy, for they recognize that to steal, even when faced with hunger, would bring reproach on God. (The Watchtower, April 1, 1984, p.28-29, subheading "Pitfalls").

The idea is, if you are caught doing something wrong, others will view it as a failure of your God and your religion instead of a failure in yourself. Thus, the reproach is seen as reflecting on Jehovah, not the wrongdoer.

We would not want anything about our appearance or way of life to bring reproach on our heavenly Father or to detract from the message we preach. (Keep Yourselves in God's Love, 2008, p.90, para.14)

Your love for Jehovah will move you to avoid committing a serious sin that would bring reproach upon his name... Be determined not to ‘assail the name of God’ by bringing reproach upon him. Instead, always strive to do upright things that bring him glory. (The Watchtower, November 15, 2006, p.21-22, para. 5).

Does consuming large amounts of alcohol ever bring glory to God? A Christian would certainly want to avoid having a reputation as a heavy drinker. Such a reputation would bring reproach on, not glory to, Jehovah’s name. (The Watchtower, December 1, 2004, p.21, para. 11)

... we do not wish to bring reproach on Jehovah’s name by being punished for wrongdoing. (The Watchtower, November 1, 2002, p.13, para.16)

However, poor behavior or thoughtless actions on the part of just a few can bring reproach on God’s name and on his people.(Our Kingdom Ministry, May 2000, p.6, para.1)

But that is a backward concept: Since the Bible states that God is always good (Mark 10:18), and humankind is not (Romans 3:23), it's obvious that the failure is on humans and not God. This is supported in the media: Unless a crime or offense is decidedly religious in nature, a criminal's religion is rarely an issue in the news. In other words, if a person is caught molesting children, usually the news story doesn't reveal which denomination the molester belonged to. And if the person committing the molestation happens to be a religious leader, it still isn't God who is called into question but the religion's practices and polices that are called into question. For example, when the molestation of children by Catholic priests first came to light, the media didn't blame God, they blamed the men in the Catholic hierarchy who did not report these incidents to the police. And in the same way, when the molestation by Jehovah's Witness elders first came to light, again the media didn't blame God but instead blamed the men in the Watchtower Society's hierarchy who also did not report these incidents. The reproach does not land on God's Name, it lands on the men in the human leadership of the religious denomination. The Watchtower Society, however, takes this a step further: Since they equate themselves with being the God's Organization, and God's sole Channel of Communication with humans on earth, they equate reproach upon themselves as being the same as reproach upon Jehovah. Essentially, they are equating themselves with God.

What is the difference between bringing reproach on oneself and bringing reproach upon God?

Reproach on oneself includes (things in which we demean ourselves):
Polygamy, divorce, cohabitation
Drunkeness and drug addictions
Robbery, burglary, and thieving
Laziness, slovenly hygeine
Immorality and adultery
Pridefulness, arrogance
Racism and prejudice
Molestation and rape
Vanity and egotism
Greed and gluttony
Lying, scheming
False Prophecy
Love of money
Causing fights

Reproach on God includes:
Swearing to God on a lie (this demeans God's name by attaching it to a lie, whereas God is always true -- Titus 1:2, Hebrews 6:18)
Praying to idols or other gods (this defames God by denying His existence in favor of a false god)
Belief in evolution instead of creation (evolution defames God by denying His existence)
Blasphemy (blasphemy demeans God's Holy Name)
Atheism (this, too, denies the existence of God)

See the difference? Reproach on God isn't merely any sin, instead it is specific sin which directly demeans or defames God. To illustrate: If a Baptist minister is caught in an adulterous affair, this reflects badly on the minister, but not God Himself, because the adultery was not attached to God, the reproach is solely on the minister and his mistress. If, however, the guilty minister lyingly swears to God that he didn't have the affair, then he is reproaching God's Holy Name because he then is attaching a wicked lie to Him; a very defamatory and demeaning action.