In 1917, the British royal family changed the name of their house from Saxe-Coburg-Gotha to Windsor because of anti-German sentiment. The king was reluctant to make this change and break with tradition. Would the monarchy have survived if he refused to do this?
Probably nothing changes, in retrospect, but at the time there were Gotha bombers in the skies over the UK and the other European monarchies were starting to crumble, so it was a good PR stunt if nothing else.