Historically, members of Royal families had no need for 'surnames', as Kings and princes were  known by the names of the countries over which they and their families ruled. Kings and queens  therefore signed themselves by their first names only, a tradition in the United Kingdom which has  continued to the present day (see style and title).

Members of the British Royal family had no surname before 1917, but only the name of the  dynasty to which they belonged.   The names of dynasties tended to change when the line of  succession was taken by a rival faction within the family (e.g. Henry IV and the Lancastrians,  Edward IV and the Yorkists, Henry VII and the Tudors), or when succession passed to a different  family branch through females (e.g. Henry II and the Angevins, James I and the Stuarts,  George I and the Hanoverians).

Just as children can take their surnames from their father, so sovereigns normally take the  name of their 'House' from their father. For this reason, Queen Victoria's eldest son Edward VII  belonged to the House of Saxe-Coburg-Gotha (the family name of his father Prince Albert). Edward  VII's son George V became the second king of that dynasty when he succeeded to the throne in 1910.