This peninsula was the first place called ‘California’ and thus the body of water on its east coast is the Gulf of California/ Golfo de California (but also known as the Sea of Cortez/ Mar de Cortés). When the Spanish missions expanded north of the peninsula (in 1769+), this northern region was called Nueva (New) California or Alta (Upper) California. To prevent confusion in letters and documents the peninsula began being called Antigua (Old) California or Baja (Lower) California.
The two Californias became part of the newly independent Mexico in 1822. In 1848, a payment for and transfer of Alta California to the United States was made official. The ‘Alta’ part of the name was dropped when California became a state in 1850. Mexico did not drop the ‘Baja’ part. The peninsula was divided into two territories and both are now states, first the north half on December 31, 1952 and the south half on October 8, 1974.
With the habit of people to abbreviate names, ‘Baja’ (or by Spanish speakers, ‘La Baja’) is common to hear and is well-known around the world. Unfortunately, this upsets some people, including many in the academic world. They are pushing for dropping ‘Baja’ from the name of the two states that make up the peninsula and a return of the original peninsula name, California, with the two states becoming North and South California (or Northern and Southern California).
Here, below, is the peninsula half with the mission names of early 1787 easily identified as written: