I have been discussing the title of the new Murakami novel, Killing Commendatore with my friend, Ursula Gräfe, the German translator. Ursula made a very interesting suggestion. She thought that perhaps given the author's interest in music, the "Commendatore" might in fact be Il Commendatore, a character from Don Giovanni. Murakami talked about Don Giovanni conducted by Karajan with Seiji Ozawa in Absolutely on Music: Conversations with Seiji Ozawa, tr. by Jay Rubin.
As many readers will know, in Mozart's opera, Don Giovanni seduces Donna Anna while wearing a mask. Donna Anna thinks he is her fiancé, Don Ottavio. When the truth comes out, her father, Il Commendatore, comes to her rescue. Don Giovanni challenges him to a duel, kills him, and escapes. Il Commendatore later returns as a a statue who comes to life and gets his revenge.
The connection to the opera would explain the use of the word "Commendatore" in the English title. A quick internet search shows that somebody on reddit also thought of that.
The word in the Japanese title, translated as "Commendatore" into English, is 騎士団長, while the character in Don Giovanni is known in Japanese as 騎士団管区長, but that doesn't necessarily mean that Ursula is wrong.
Don Giovanni (Elliot Madore) duels the Commendatore (Nicholas Masters) in Act I of DON GIOVANNI at the Academy of Music.