A duchess was the female married spouse of a duke.
Jessica Atreides
The only such named Duchess in the Old Imperium was the Lady Jessica Atreides, who was elevated and named to the title as administrator of Caladan after her son's, Paul Atreides', ascension to the Golden Lion Throne.
The Corrino Emperor Shaddam Corrino IV had given the planet temporarily to his childhood friend, Count Hasimir Fenring, during Leto's absence on Dune. After the Ascension of House Atreides, and the subsequent banishment of Shaddam and Hasmir to the prison planet of Salusa Secundus, Paul put the Ecazi Prince Xidd Orlaq as administrator of the water world.
After Paul and Jessica's visit in 10,197 AG to Caladan, Paul decided the planet Caladan needed a wise and just ruler, with someone who was familiar with the world's population, as Orlaq decided he wanted to return to Ecaz. Although Jessica had been just a bound concubine, Jessica was given the title of Duchess because her long devotion to dead spouse, Duke Leto Atreides I; and of course, because she was the Emperor's mother.