Stretching the thread a bit but earlier this year we visited my wife's great uncle's grave at the CWGC Lancashire Landings cemetery on the Gallipoli peninsular. He too had no personal inscription on his headstone. Same answer from the CWGC, 'his relatives probably did not want an inscription.' Interestingly the headstones are laid down sloping out there because of the danger of earthquakes disturbing more vertical memorials.
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