Metonymy [meh-TAHN-uh-mee] is a figure of speech that substitutes a word or phrase that stands for an object, action, institution or the like for the object itself. For example, in the phrase “surf and turf”— in the context of restaurant fare—surf is a metonymy for seafood and turf is a metonymy for beef.
In a different context, the word turf is a common metonymy for the institution of thoroughbred horseracing:
One of the most famous jockeys in the history of the turf a century ago was Sam Chipney, who was “jockey for life” to the Prince of Wales, at a salary of $1,000, and retired from the turf with his royal master in 1791. Home and Country, Volume 9, Monthly Illustrator Publishing Company, 1894.
Here are some more examples of metonymy from various sources:
Tories were American colonists who remained loyal to the Crown during the American Revolutionary War.
Crown = “the British government.”
Suits stars Gabriel Macht as Harvey Specter and Patrick J. Adams as Mike Ross—lawyers at a high-powered New York law firm. (Suits is the title of a television series.)
Suit = an authority figure such as a lawyer or FBI agent.
Ready for another cup?
cup = a cup or mug filled with coffee
The pen is mightier than the sword.
pen = written form of persuasion
sword = military action
Friends, Romans, countrymen: Lend me your ears.
ears = attention
Lamb and potatoes: a dish fit for a king
dish = a meal
France, less favoured on the whole as to matters spiritual than her sister of the shield and trident, rolled with exceeding smoothness down hill, making paper money and spending it.
This quotation from A Tale of Two Cities contains more than one layer of figurative language.
France = the people of France.
France is also being personified as a woman with a sister.
sister of the shield and trident = Britannia, ergo, Britain.
A common symbol of the nation of Britain is the image of Britannia—a seated woman holding a shield and trident. The shield she holds represents military might, and the trident represents sea power. The trident is associated with the sea because it was the emblem of Poseidon, the god of the sea in Greek mythology.
Reading fluency requires background knowledge that enables readers to interpret the use of metonymy and other figurative language.
And a word used as a metonymy is a metonym (MET-uh-nim). So you could say:
“In a different context, the word turf is a common metonym for the institution of thoroughbred horseracing…”
Though you can certainly use metonymy or the word itself, and metonym seems to be a backformation (if a pretty old one). It seems like metonym is more commonly used used than metonymy, but that’s just my impression.