New Orleans is named for a regent of France, and the name is fairly literal: a new Orléans on the Mississippi.
The city was founded in spring 1718 by the French Mississippi Company under Jean-Baptiste Le Moyne de Bienville, the governor of Louisiana. Wikipedia reports that he chose a spot of relatively high ground on a bend of the Mississippi, beside a portage to Lake Pontchartrain. The settlement was called La Nouvelle-Orléans in honor of Philip II, Duke of Orléans, who was then regent of France.
The duke's title came from the French city of Orléans. Wikipedia says that city was originally called civitas Aurelianorum, possibly after a Roman emperor, and that the name evolved into Orléans over time. So the chain runs backward in layers: a Roman-era name, a French city, a ducal title, a regent, and a colony on the Mississippi.
Language changed with the flag. Spain, which took over the colony, called the city Nueva Orleans until 1800. The United States acquired it in 1803, and the name was anglicized to New Orleans.
The area had a Choctaw name too. Wikipedia gives Bulbancha as "land of many tongues." The 64 Parishes encyclopedia calls that meaning approximate, "the place of other languages." It cites the Choctaw linguist Jason Lewis, who reads the word as a contraction of balbáha a̱shah, "speakers of foreign languages are there." Le Page du Pratz wrote in the 1750s that the name referred to the river itself. 64 Parishes calls that reading questionable, since the contact happened on land. The modern use of Bulbancha for the city dates from 2014.
The sources say plainly that the city was named for the regent. They do not say why that name was preferred over a local one, so the reasoning behind the choice remains unrecorded here.