Actually, they've asked that the names NOT be released last time I checked, as they're afraid that any form of bullying or vigilante justice against them wouldn't be what she wanted.
Well, the only choice the police have at this point is to engage in a case against them if they know the suspects' identities. Otherwise, the names WILL be released to the public and shit WILL hit the fan for them. The fact that a gang rape could occur with no convictions AND the picture of the rape being freely allowed by the police to be passed around the community with a "not our problem" justification ruins any trust the locals have in their law enforcement and government. Good things don't happen when you can't trust the people who are supposed to protect you.
In this case, I think vigilante justice would be better than no justice at all. This isn't exactly something to be swept under the rug, and if the government can't deliver justice, SOMEBODY will whether they like it or not. Right now they're facing a choice between either engaging in a prosecution and putting some people in prison or allowing them to be lynched.
If all goes well, the suspects will be so scared of retribution that they voluntarily confess.