“La Jolla” is pronounced /la'hoja/ not /la'hoza/, as one might expect due to the pronunciation of the orthographic “ll” in the Spanish of most of Latin America.
The area was known as “La Jolla Park” at least as early as 1886.
The origin of the name is obscure. Some say it is a corruption of “ahoy”, called out by sailors seeking the attention of people on the shore.
Promoters of La Jolla claim it is from the Spanish “la joya”, meaning the jewel. A more likely though less glamorous theory is that “La Jolla” is a corruption of the Native American word “Woholle”, meaning hole in the mountain, referring to the caves in the north-facing cliffs next to La Jolla Cove Park.
Most of these have since either collapsed due to ongoing erosion, or have been intentionally destroyed by local authorities to prevent the drownings that were once frequent occurrences.