1960 - By Proclamation Queen Elizabeth II formally confirmed that she and her children would continue to be known as the 'House and Family of Windsor' as would any descendants who carry the style of Royal Highness and the title of Prince or Princess. Also in the Proclamation the Queen decreed that her descendants who do not have that style and title would bear the surname Mountbatten-Windsor.
Any future monarch can change the dynastic name through a similar royal proclamation as royal proclamations do not have any statutory authority.