While I agree with what WhiteFire is saying in regards to the dangers of libel and defamation and the need to protect people from the malicious destruction of their character without basis in facts, I think this law can be a dangerous move and I'd very much like to know whom the exposed identities would be revealed to. When you're talking about a country that is involved in armed conflicts in a very dangerous part of the world, where ideas and words are as powerful as bullets in steering politics, the danger is that getting a court to reveal someone's identity may be all their opponent needs. Maybe they don't need to win a frivolous court case--maybe they only need to know what that person's name is, where they live, where their children sleep... And in the case of big companies or groups, they may not need to go to such extremes. Just bringing a case against someone will force that person to pay a lot of money and lose a lot of time for work, not to mention the effects of stress on their health. A lot of people would rather be quiet than have their lives turned upside down like that. The law could be used to cudgel free speech without ever letting the cases reach the courts.
I think that revealing online identities without first proving that libel or defamation has actually occurred could put the accused in very real danger. On the other hand, actual cases of libel/defamation should certainly be prosecuted, and how could one prove it one way or the other without first locating the libeler?
Here in the US of A, a person has a right to face their accuser. Do they also have a right not to, if they don't want to see them, or be known to them? And how about in Israel? And to the repeated statement that there will be restrictions and regulations, well... that's like saying we've got a screen door so we should be good in a rainstorm, eh? Lawyers will find ways to manipulate or avoid such things, and most of the time breaking a regulation in a bureaucracy will get you only a slap on the wrist, while the person you use it against could lose everything. Sure, several years of appeals and lawyer fees and misery later, you might get them to admit that they did something they shouldn't have. But by then you've spent a great deal of time and energy and money to get right back to where you started.
I'm not denying that libel and defamation are serious crimes that can cause a lot of damage. But I don't think this law is the right way to address them--I think it will cause a lot more problems than it solves.