I think that is premised on the assumption that (a) the shooter is looking for "fame" or (b) copycat killers are less likely to idolize a 'faceless' shooter than a named entity they can focus on.
I don't know if all those factors are present in these shootings. Instead, there could be upside in exposing the shooter, his situation, and his family (which may or may not be fair to them) in order to figure out what happened, what signs (if any) were missed, and possibly raise awareness so someone in the future heads off a future tragedy.
I don't know the answer. It's f'd up. But too often reasonable ideas might not stop wholly-unreasonable people from doing what they are going to do.