Sappho is an ancient Greek poet who is recognized for her lyric poetry which has survived in fragments. She was born on the island of Lesbos.
Lady Mary Montague, a contemporary of Pope and friend of Samuel Johnson and other writers of the 18th Century, is called "Sappho" in Pope's "Epistle". Montague was a woman of intellect and wit, and is best remembered for her letters. An "epistle" is also another word for "letter".
In Pope's "Epistle," he uses all Greek names--goddesses and famous characters--to illustrate the way women should behave. Although Pope is frequently called a misogynist, he was an amazing critic of the age. The Epistles are meant to guide women away from the stereotypical foolishness for which women were known and criticized--vanity, stupidity, emotional instability and illogical thinking. Pope's poem illustrates that women are complicated creatures--not consistent or predictable at all as males are.
Sappho is sarcastic, Silia rages over a blemish, Papilla wants shade but detests trees, repulsive Calyso attracts by cunning, Narcissa is mentally unstable, Flavia is prone to depression, and Atossa is violent and emotional.
By using these characters (probably all aligned with a living female whom Pope knew or knew of) he displays all of the stereotypical flaws in a female, thus instructing any woman who reads the grouping of poems how "not" to be.