I'm sorry, but domestic abuse is wrong, it's against the law, and we shouldn't help the abusers keep what they're doing a secret. Also, printing abusers' names in the paper will make their victims confront the issue. We've all heard stories of abused wives living in terrible situations for years because they thought they were alone, in the wrong, co-dependent, etc. Community knowledge of the abuse will make it very difficult for these wives to hide from their situation. They'll have to confront it.
Social accountability is a good thing.
Men and women who are exposed as domestic abusers will be held accountable in the community. They'll immediately lose respect and social status. They could likely lose friends and be ostracized. Maybe they'll finally face their own problems. Many abusers were abused themselves.