The Saxe-Coburg-Gotha title came courtesy of Prince Albert and was proudly held throughout the Victorian and Edwardian age. But then World War I broke out and Germans (and the names they came with) weren’t terribly popular in Britain. Things got really bad in March 1917 when a heavy aircraft capable of crossing the English Channel began bombing London. It was unfortunately named the Gotha G.IV. Not long after, the Tsar of Russia abdicated, creating a ripple of fear throughout Europe’s royal families, which worried about their own positions. So, to appease the people and possibly save their jobs, the royal family agreed to abandon all their German titles (and there were many—after all, the family was descended from the Hanovarians) and Anglicise their name.
Windsor it was, and Windsor it remained, even after Princess Elizabeth married Prince Philip of Greece and Denmark, who belonged to the House of Schleswig-Holstein-Sonderburg-Glücksburg (which must have been a nightmare to learn how to spell when he was a kid). He adopted the surname Mountbatten, but Elizabeth and their children retained the name of Windsor.