The New Orleans krewe whose name is Latin for “king” is Rex.
Rex is the short name of the Rex Organization, one of New Orleans’ best-known Carnival krewes. The Latin word rex means “king,” and the organization’s monarch is traditionally styled the King of Carnival. Its daytime parade is held on Mardi Gras Day.
Rex was founded in New Orleans in 1872, partly to stage a grand spectacle for Grand Duke Alexei Alexandrovich of Russia, who was visiting the city during Carnival season. The organization also hoped to encourage tourism and commerce after the Civil War.
Rex is not the same as the other names listed in the question. Orpheus, Endymion and Proteus are also New Orleans krewes, but their names come from different mythological or classical references. Rex is particularly associated with its royal title, its historic parade and the development of Mardi Gras traditions such as the official purple, green and gold colors adopted in 1892.