In some cases, they do NOT have all this information; for example, one of the cases I tracked included NOK who (due to the war situation) had moved to another address, & the Service unit (& subsequently which linked to CWGC of course) never received a reply, so no other amplifying details could be added.
Over the last few years, I have had to notify CWGC of numerous corrections / omissions; in all cases, after the verifiable source documents have been provided (& some of the casualties have not been relatives in any way), suitable amendments have been made.
The example I gave (A LUCAS) = no full name. As such, unless someone notifies CWGC (& with the proof of circumstances), nothing will be actioned to reflect his full name to go (a) in the records & (b) for his gravestone to be amended. He died for his country, he deserves that full recognition. I have ordered a copy of the death certificate which should allow that to happen.
He married Iris E Langford in 1939 &, on location probability (needs to be verified if necessary), he was born in 1917.
Nothing I can find in the UK National Archives (& incidentally, for signed-in users, digital records are free to download during the current lockdown) & unfortunately, the curator of the Royal Norfolk Regimental Museum is working remotely = no access to records. I have, via this pay per view website, got a copy of his burial record in Cambridge Cemetery, which I will forward to CWGC:
