As a society, at this time, we should understand that we will not be able to have a non-acrimonious debate about what gun control, or mental health policy, would have stopped the massacre in Connecticut. However, I believe POTUS could personally request media organizations no longer report name, or identifying imagery, of the suspected perpetrators of these crimes. Similiar to media voluntarily withholding the name of sexual assault victims.
We can perhaps discourage future massacres by letting potential perpetrators know they will remain as anonymous as possible, while having their constitutional rights met. Any one who desired could find out the name of the suspect in court documents, media organizations would only ever say the "suspected killer," while giving other relevant info.