From the Emperor’s Desk: This is the information I discovered.
The Treaty of Union and the subsequent Acts of Union state that England and Scotland were to be “United into One Kingdom by the Name of Great Britain”, and as such “Great Britain” was the official name of the state, as well as being used in titles such as “Parliament of Great Britain”.
The websites of the Scottish Parliament, the BBC, and others, including the Historical Association, refer to the state created on May 1, 1707 as the United Kingdom of Great Britain. Both the Acts and the Treaty describe the country as “One Kingdom” and a “United Kingdom”, leading some publications to treat the state as the “United Kingdom”. The term United Kingdom was sometimes used during the 18th century to describe the state.
The Acts of Union 1800 were parallel acts of the Parliament of Great Britain and the Parliament of Ireland which united the Kingdom of Great Britain and the Kingdom of Ireland (previously in personal union) to create the United Kingdom of Great Britain and Ireland. The acts came into force on January 1, 1801, and the merged Parliament of the United Kingdom had its first meeting on January 22, 1801.
George III was King during this transition.
In Great Britain, George III used the official style “George the Third, by the Grace of God, King of Great Britain, France, and Ireland, Defender of the Faith, and so forth”. In 1801, when Great Britain united with Ireland, he dropped the title of king of France, which had been used for every English monarch since Edward III’s claim to the French throne in the medieval period. His style became “George the Third, by the Grace of God, of the United Kingdom of Great Britain and Ireland King, Defender of the Faith.”