Sarah Fortune is her real name, Miss Fortune is made to sound like misfortune.
This relates to the old sailor myth that women on ships were bad luck.
Her Ultimate's name, Bullet Time, is based off of a term used in movies in which all action goes into slow-motion, a term coined by the Max Payne video game franchise.
Her matched pistols ('Shock' and 'Awe') are a reference to a military tactic which dictates the use of overwhelming firepower and battlefield awareness to drain the enemy's will to fight back.
Miss Fortune was one of the champions available to be chosen for the Noxian pool during the 2nd Ionia vs. Noxus match. She was one of the selected champions.
Miss Fortune could be a reference to Rue Meridian from "The Voyage of the Jerle Shannara" books by Terry Brooks. Rue Meridian is an airship crew member/mercenary that "is capable of charming any man". They are also visually similar. Gangplank may be visually based off her brother, a captain of the ship.
Her Road Warrior Miss Fortune skin closely resembles the post-apocalyptic clothing worn by people in the same movie.
The sawed-off double barrel shotgun design for the skin might have been inpired by Max Rockatansky's sawed-off double barrel shotgun from the same movie.
Relations
Miss Fortune is searching for the person who killed her mother, a man with red eyes.
Miss Fortune has a strong distrust for pirates and she finds herself constantly bickering with the infamous Gangplank (the only captain to resist her charms) over the direction of Bilgewater politics.
Miss Fortune defeated Gangplank in the Bilgewater GrugMug Grog Slog competition.