Cecily Adams, who plays Ann Dunn, Murphy's "Secretary #86," was the daughter of Get Smart (1965) star Don Adams, whose character was Maxwell Smart, Secret Agent 86. Although the casting of Cecily Adams as the secretary with the same number as her father's character was a coincidence, it was noted by the producers, and Don Adams visited the set during taping.
Secretary #86 introduces herself as Ann Dunne.
Per the title, Florence Nightingale, who came to be known as "The Lady with the Lamp", was a pioneering nurse, writer, and noted medical statistician. She tended wounded soldiers in the Crimean War and became an advocate for care of the wounded soldier.