What might "a named reinternment" be? I assume return to the original grave, but with the appropriate headstone. One of the founding principles of the Imperial (now Commonwealth) War Graves Commission was that "there should be no distinction made on account of military or civil rank, race or creed".
Arguably, that could mean that anyone who believes they have identified a casualty who is only "known unto God" could ask for a DNA test - that could stretch the Commission's resources too far.