Abusers instill fear through physical and emotional threats. It's hard to testify against your abuser because of fear that is sometimes present from birth.
Fear can only be cast off with faith. You need faith in your own worth as a child of God. You are worth saving. Your abuser will continue to have a hold on you until you choose faith and courage over fear. Is it worth it to cower when you can save yourself, perhaps your children, and future victims?
You gain confidence when you withstand abuse. You gain confidence when you help yourself and others escape abuse. You gain confidence when you speak up for yourself.
Speaking up is the only way to prevent future abuse. When you speak up, other victims may speak up. Other victims may remember their abuse when their minds are ready to face the memory.
Let the Spirit guide you when, where, and to whom you tell.
Who needs to know who your abuser is? (1) Parents and children exposed to a child abuser need to know. This way parents can determine if their children were abused or prevent their children from being future victims. (2) Religious leaders need to know who the abuser is. These leaders have the responsibility to help victims, to call the abuser to repentance, and to keep the abuser away from situations with children at church. (3) Legal authorities often need to know who the abuser is. Legal authorities need to have as much evidence as they can to prosecute any abuser. Sometimes you may not have enough evidence to convict, but you are leaving a paper trail. That paper trail lends credibility to another victim's testimony. It may lead to a future conviction.
Victims who speak up hold their abusers accountable--on earth and in heaven. You serve as a witness to their sins. This is the only way for them to receive earthly justice. Also, abusers can use this opportunity to repent (not to be trusted again). Many won't, but they need that opportunity.
Some victims may want to exact revenge (self-defense is just fine). Vengeance is never satisfied. Only legal authorities and God should exact vengeance (see D&C 64). If you never forgive, you are holding onto a weight that is sapping your energy. You wield courage when you forgive and you gain confidence.