What is the full name of the city of Los Angeles, California?

El Pueblo de la Reyna de Los Angeles (The Town of The Queen of Angels)

==== refer Encyclopaedia Britannica

There is a lot of controversy over the exact "original" name and there are lots of variations, as this article points out:

http://articles.latimes.com/2005/mar/26/local/me-name26

It appears that the following is the best we can do:

El Pueblo de la Reina de Los Angeles (The Town of the Queen of the Angels.)

Contrary to the popular belief that the original name of Los Angeles was El Pueblo de Nuestra Senora La Reina de Los Angeles de Porciuncula (The Town of Our Lady the Queen of the Angels of the ((River)) Porciuncula), scholars have determined from official documents of Governor Felipe de Neve, Commandant General de la Croix and Viceroy Bucareli that the settlement was simply named El Pueblo de la Reina de Los Angeles (The Town of the Queen of the Angels.)
[Source: Mexican Los Angeles by Antonio Rios Bustamante, Floricanto Press, 1992]

http://www.laalmanac.com/history/hi03b.htm

"You see it at the top of the map, 'El Pueblo de la Reyna de los Angeles.' That's the name on the first handwritten map in 1785. You have to look at the original documents, and that's what we've done. The name is right there." The map uses "Reyna"; other sources spell it "Reina."

http://articles.latimes.com/2005/mar/26/local/me-name26

As local lore tells it, on September 4, 1781 the 44 pobladores gathered at San Gabriel Mission and, escorted by a military detachment and two priests from the Mission, set out for the site that Crespí had chosen. In reality, several of the families were probably already working on their plots of land as early as late July.[6] Governor de Neve gave the new town the name El Pueblo de la Reina de los Ángeles-The Town of the Queen of the Angels.

https://en.wikipedia.org/wiki/Pueblo_de_Los_%C3%81ngeles

Father Crespi had picked out a site along the river for a mission, but in 1771 Father Serra had the Mission San Gabriel Arcángel built near Whittier Narrows. After a 1776 flood, the mission was moved to its present site in San Gabriel. The Mission Nuestra Señora Reina de los Angeles was established on September 4, 1781 by a group of 46 Spanish and Mexican settlers from Sonora who had set out from the San Gabriel mission to establish a settlement along the banks of the Porciúncula River. These settlers were of African, Indian, and Spanish ancestry of which two-thirds were mulatto. "Colonial records indicate that twenty-six of the forty-six original settlers of Los Angeles were of African or part-African ancestry" [de Graaf, L. Seeking El Dorado:African Americans in California].

The new governor of California, Felipe de Neve, recommended to the viceroy in Mexico that the site be developed into a pueblo (town). The area was duly named "El Pueblo de Nuestra Señora la Reina de los Angeles del Río de Porciúncula," ("The Town of Our Lady the Queen of the Angels on the River Porciúncula"). It remained a small ranch town for decades, but by 1820 the population had increased to about 650 residents, making it the largest civilian community in Spanish California. Today the outline of the Pueblo is preserved in a historic monument familiarly called Olvera Street.

https://en.wikipedia.org/wiki/Los_Angeles,_California

Good answer, very detailed.

During Spanish rule of the Californias, a pueblo was established to help supply garrisons and other outposts. The city got it's name, circuitously, from the Los Angeles river, along with some embellishment from a chapel near Assisi, Italy. It's original name was "El Pueblo de Nuestra Señora la Reina de los Angeles de Porciúncula" or The Town of Our Lady the Queen of Angels of the Little Portion, although its official name was simply El Pueblo de la Reina de Los Angeles.
Simplicity indeed. Los Angeles is mouthful enough.
http://www.laalmanac.com/history/hi03a.htm

When Spanish occupation of California began in 1769, an expedition of more than 60 persons led by Gaspar de Portola moved into the area now known as Los Angeles. They camped by a river where fertile soil and availability of water for irrigation impressed members of the party. Father Juan Crespi, who accompanied the group, named the river El Rio de Nuestra Senora la Reyna de Los Angeles de Porciuncula, which means "The River of Our Lady the Queen of the Angels of Porciuncula. "


12 years after Portola's trek, which began in San Diego and ended in Monterey, a company of settlers called "Los Pobladores" were recruited in the states of Sonora and Sinaloa in Mexico. Their mission, under authority of Governor Felipe de Neve, was to establish pueblos (communal villages) in the name of the king of Spain.

On September 4, 1781, the Pobladores, a group of 12 families - 46 men, women and children led by Captain Rivera y Moncada - established a community in the area discovered by Portola, and named it El Pueblo de Nuestra Senora la Reyna de Los Angeles de Porciuncula, after the nearby river. Over time, the area became known as the Ciudad de Los Angeles, "City of Angels," and on April 4, 1850 became the City of Los Angeles.

Los Angeles was founded in 1781 by the Spanish governor Felipe de Neve as "El pueblo de Nuestra Señora Reina de los Angeles de Porciuncula".