I've been watching playthroughs of the more primitive Donkey Kong games on YouTube and it occurred to me, if these games predate Super Mario Bros., the Mushroom Kingdom and Princess Peach, then who is the woman that Donkey Kong abducts and Mario sets out to rescue?
"Pauline" or "The Lady" or "The Beautiful Girl"
The original (1981) arcade game has this bumper on the side
"Jumpman saves the lady"
Note that Mario hasn't been given a name (yet) and his back-story has him as an elderly carpenter, not an Italian plumber.
Press adverts from early 1982 simply call her 'The Beautiful Girl'
The name Pauline was applied to various merchandise that was sold to promote the NES games in Japan in 1982/3, including these plastic models.
The earliest source that names her as Pauline seems to be this (1982) Nintendo colouring book that accompanied the game and provided some back-story for her abduction.
She was also named in the 1983 cartoon Saturday Supercade.
Canon confirmation was provided when she was officially named in the manual for the English-language NES version of Donkey Kong in 1986, and she seems to have retained the same name ever since.
Other sources refer to her as The Lady, The Girl or Mario's Girlfriend.
Interestingly, she was given a different name in a print ad for the (1982) Game and Watch version of Donkey Kong ("Donkey Kong, the famous monster ape holds lovely Louise prisoner") but that appears to have been an invention of whoever wrote the copy for the advert.
Pauline was created by Shigeru Miyamoto and other developers for the 1981 arcade game Donkey Kong. She is the first female character in a video game with a speaking role, and is cited as a famous example of a damsel in distress in fiction. Originally, Pauline was known as Lady, and the game introduced her as Mario's girlfriend. The name Pauline was given after the then-girlfriend of Nintendo of America's warehouse manager, Don James. It was then used in licensed products after the game's release (including a collection of figures by Coleco and a coloring book), and was eventually used for the NES version of the game, although print ads for the Game & Watch version of the game refer to her as Louise. Captured by Donkey Kong atop a New York City construction site, the official artwork depicted her disheveled like the 1930s King Kong's Fay Wray in a torn dress and stiletto heels.