As shown in the film, the real King George V did change his last name from Saxe-Coburg and Gotha to Windsor as a result of anti-German public sentiment. He was the father of King George VI, grandfather of Queen Elizabeth II, and great grandfather of King Charles III.
The first panoramic views of the trenches with the voiceover of The Shepherd, particularly the depiction of mountains of spent shell cases, are taken from real photographs of the Battle of The Somme. Fought between July and November 1916, with no clear winner, it cost the lives of around 700,000 British and French soldiers and 550,000 Germans. As shown, entire battalions were mowed down with machine gun fire and over one million shells were fired in the first week alone.
General Kitchener's line "The objective of war is not to die for one's country, but to make the enemy die for theirs!" is a far more refined version of a real line by WWII General George S. Patton on a speech to the men of the Third U.S. Army on May 31, 1944. The actual line goes: "No bastard ever won a war by dying for his country. He won it by making the other poor dumb bastard die for his country."
At one point Conrad shows his father a white feather, given as a symbol of cowardice for not fighting in the war. This was a real-life practice: the Order of the White Feather was a club that publicly humiliated men into military service by directly giving/sending them white feathers. The Order was devised by Admiral Penrose-Fitzgerald to boost recruitment and patriotism. While effective, sometimes the wrong people got targeted. For example in one incident a wounded serviceman receive a feather on his way to the reception for his decoration.
Oxford's flashback scene takes place during the Battle of Ginnis on December 30, 1885. This was the last battle fought by the British in their historical Red Coats.