I think this is an issue outside of the police. In the Suffolk murders case the first man detained was at no point named by the police.
The media did all the hyping and I remain very sceptical of the BBC for playing the audio tape of the first man. So for me this is not about the police, its more to do with the "freedom" of the press to report things "in the public interest"
On balance, if the press behave responsibly, I would rather see a press which is as free as possible to report items which at times can go to the heart of Goverment. journalism at its very best requires freedoms.