That’s just the kingdom of England and Wales, which has existed since the 11th century.
The Kingdom of Great Britain was created in 1707 with the acts of union in England and Scotland.
Then the act of union in 1801 joined the Kingdom of Ireland with the Kingdom of Great Britain to form the United Kingdom of Great Britain and Ireland.
So if Scottish independence actually happens they’ll leave behind The United Kingdom of England, Wales and Northern Ireland.
Scotland and Ireland can then form the Greater Union of Celtic Republics and of course Wales and Northern Ireland would be more than welcome to join us.