The History of Cardenio is known to have been performed by a theatre company who assumed a new name in 1603 when what monarch took the throne?
The History of Cardenio: The History of Cardenio, often referred to as merely Cardenio, is a lost play, known to have been performed by the King's Men, a London theatre company, in 1613. King's Men (playing company):  Formerly known as The Lord Chamberlain's Men during the reign of Queen Elizabeth I, they became The King's Men in 1603 when King James I ascended the throne and became the company's patron.
King James I