Oh names - yes - forgot
governed by Letters Patent - Victoria was a Hanoverian ( but lost out on german possessions in Hanover which went to men ) except Heligoland which she sold 1860 I think
Victoria married and became the first Saxe Coburg Gotha. George V d.1935 the first to use 'Lilibet', more famous for using bagga bognor as his last words, changed the Name to Windsor 1917.
and so..... when Lilibet married Phil the Greek Prince of Greece and Denmark, Lds Louis Mountbatten ( note surname) was VERY keen that the house name should change to Mountbatten Windsor
Literally no one else was in the country
and so in 1962 - they decided that the House of Windsor cd call itself what it liked and stayed with Windsor. House OF Windsor note so the Royals have no surnames ( unlike Tudors and Stuarts)
AND
anyone in need of a surname, wivvart a title could take Mountbatten-Windsor. Hence Archewell and Lilibet M-W
Christian names - no rules but Edward as the name of a King isnt a great winner ( Edw VI - died young - Edw VII notorious luch, Edw VIII m a woman with two husbands still living, and was a nazi )
Oliver - whoopsie - I thought Diana was 'persuaded' no. No one has tried 'adolf' - - yet
usually it is agreed.