The scene in Love Me Tonight where Maurice, a common tailor, encounters the princess Jeanette, is smitten, and addresses her as "Mimi" in song, is a bit silly but delightful. After all this is a musical, not real life. And actually, I think it started a trend that was copied in subsequent shows.
In the '49 Gentlemen Prefer Blondes, Coles and Atkins sing about a gal, a miss from Mississippi, whose name was Mame, but now they call her Mimi, because (after all) she's the toast of the Rue de La Paix. Those Frenchmen!
In '56 Tony Esposito in The Most Happy Fella encounters a waitress named Amy, is thunder struck, invites her to his Napa Valley farm, and calls her Rosabella. Those Italians!
Starbuck in the '63 110 in the Shade meets the lonely spinster Lizzie Curry and calls her Melisande for one night. Those Americans!
When Don Quixote in the '65 Man of La Mancha comes upon the kitchen slut Aldonza, reeking of sweat, he renames her Dulcinea. Those Spaniards!
Hey, whaddaya know! It's universal. And all because Rodgers and Hart wrote "Mimi" for Maurice to sing to a girl named Jeanette. Go figure.