How did the Royal family announce it to the public? Was there any anger towards the monarchy either for being of German decent or changing it the first place?
The change was announced via royal proclamation on The London Gazette 17 June 1917 https://www.thegazette.co.uk/London/issue/30186/page/7119 The change was enacted to eliminate the aura of Germaness that surrounded the royal family. The queen's brothers also abandoned their foreign titles at this time and Louis of Battenberg became Mountbatten.