I used to work in the justice system and and my job was liaising and briefing the media on high profile cases, so I've got a bit of experience in this area. I can see both sides of the argument for naming and not naming, but on the whole, I think we have the balance about right in England when it comes to the way we handle child prosecutions generally. I have managed media relations around a case where a child murdered another child and certainly got a crash course in every ethical and legal dilemma that this entails.
Ultimately, though, I think it's probably right that they are named. Not because I think the subsequent furore will be even remotely edifying - it won't, it will be awful - but for purely practical reasons, it simply doesn't make a whole lot of material difference.
Firstly - the media, of course, do already know the murderers' names - there will have been journalists in court reporting on the trial. So if they want to start digging around for info on their families etc, they'll have already done that. There's a lot of information they could plausibly share about them and their families even without naming them.
Secondly - everyone local to the case (neighbours, classmates, friends etc) will also obviously know their names too. If the police announce that a child has been charged with murder, and a child of that age and gender then suddenly disappears from school and the family home for many months, it's not hard to work out that they're the suspect.
Thirdly, when the perpetrators are released, they will get new identities regardless of whether they're named publicly anyway. Their families will also suffer and likely need protection whether they are named or not.
Fourthly, while it is certainly true that the families of underage murderers will suffer from being known as such, this is also the case for the families for the case of adult murderers - but we routinely name adult murderers. So I think if we don't name a child who has committed murder because we need to protect their parents and siblings, in the interests of fairness we would also have to stop naming adult murderers too, for exactly the same reason. The younger sibling of a teenage murderer will absolutely have a hard time and will likely need to relocate and change their name and all sorts of other things - but this is also true of, eg, the younger sibling (or child) of an adult murderer. If we protect one set of families and throw the other set to the wolves, then the system is fundamentally unfair.