Question: What is the formal name of the nation of Hawai which Peter Cushman Jones was a businessman and politician in

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Monkwearmouth–Jarrow Abbey: Monkwearmouth–Jarrow was a twin-foundation, English, Roman Catholic monastery, located on the River Wear in Monkwearmouth and on the River Tyne in Jarrow, respectively, in the Kingdom of Northumbria and historic County Durham (now in the metropolitan county of Tyne and Wear, England).  Its formal name is The Abbey Church of Saint Peter and Saint Paul, MonkwearmouthJarrow.  Jarrow became the centre of Anglo-Saxon learning in the north of England, producing the greatest Anglo-Saxon scholar, St. Bede.  It was confiscated from the Roman Catholic Church by King Henry VIII during his dissolution of the monasteries in the 16th century, and subsequently fell to ruin.  The twin monastery was the UK's nomination for World Heritage Site status in 2011.

Hapoel Beit Lid F.C.: Hapoel Beit Lid F.C. (Hebrew: הפועל בית ליד‎ ‎ ), was a football club from the Beit Lid Ma'abara (temporary immigrant camp), Israel.  The club was also rarely referred to as Hapoel Shvut Am (Hebrew: הפועל שבות עם‎ ‎ ), as Shvut Am (lit.  "The Nation Returns") was the formal name of the camp.

Guaymas: Guaymas (] ) is a city located in Guaymas Municipality in the southwest part of the state of Sonora in northwestern Mexico.  The city is located 117 km south of the state capital of Hermosillo, and 242 miles from the U.S. border, and is the principal port for the state.  The municipality is located in the Sonora Desert and has a hot, dry climate and 117 km of beaches.  The municipality’s formal name is Guaymas de Zaragoza and the city’s formal name is the Heróica Ciudad de Guaymas.

Caldoche: Caldoche is the name given to European inhabitants of the French overseas collectivity of New Caledonia, mostly native-born French settlers.  The term "caldoche" has a pejorative connotation.  The formal name to refer to this particular population is "Calédoniens ", short for the very formal "Néo-Calédoniens ", but this self-appellation technically includes all inhabitants of the New Caledonian archipelago, not just the Caldoche.  Another "white" demographic element (although they may well be French people of different ethnic backgrounds) in the territory is expatriates from metropolitan France who live there temporarily as civil servants.  Caldoches are keen to differentiate themselves from these inhabitants, underlining their position as the permanent locals, referring to them as "métros " (short for "métropolitains ") or as "Zoreilles" (informally "zozos ") in local slang.

Trivial name: In chemistry, a trivial name is a nonsystematic name for a chemical substance.  That is, the name is not recognized according to the rules of any formal system of chemical nomenclature such as IUPAC inorganic or IUPAC organic nomenclature.  A trivial name is not a formal name and is usually a common name.

Peter Cushman Jones: Peter Cushman Jones (October 12, 1837 – April 23, 1922) was a businessman and politician during the Kingdom of Hawaii, Provisional Government of Hawaii, Republic of Hawaii and Territory of Hawaii.

Lilou: Lilou is a French female given name.  It is rising in popularity in France, where it is ranked in the top 50 names given to baby girls.  It may have originated as a short form of names ending in the sound "lee" such as Aurélie, Amélie, Aline, Élise, Élie, Coralie, or Liliane, following the French way of forming short forms of names by adding the suffix "ou" to affectionate names.  It is also said to be an Occitan language version of the name Lily, originally spelled Liló in that language.  It was not registered as a formal name in France prior to 1997, when 19 girls named Lilou, nine girls named Leeloo and four girls named Leelou were registered.  The spelling Lylou is also used.  Short forms of names have become increasingly popular as formal names in France as well as elsewhere in Europe.

Flies' graveyard: Flies' graveyard and flies' cemetery are nicknames used in various parts of the United Kingdom for sweet pastries filled with currants or raisins, which are the "flies" in the "graveyard" or "cemetery".  In Scotland, the formal name is "fruit slice" or "fruit squares".  In Northern Ireland, the formal term is "currant squares".  In the North East of England, they are called "fly cakes" or "fly pie".

French Forces of the Interior: The French Forces of the Interior (French: "Forces Françaises de l'Intérieur" ) refers to French resistance fighters in the later stages of World War II.  Charles de Gaulle used it as a formal name for the resistance fighters.  The change in designation of these groups to FFI occurred as France's status changed from that of an occupied nation to one of a nation being liberated by the Allied armies.  As regions of France were liberated, the FFI were more formally organized into light infantry units and served as a valuable manpower addition to regular Free French forces.  In this role, the FFI units manned less active areas of the front lines, allowing regular French army units to practice economy of force measures and mass their troops in decisive areas of the front.  Finally, from October 1944 and with the greater part of France liberated, the FFI units were amalgamated into the French regular forces continuing the fight on the Western Front, thus ending the era of the French irregulars in World War II.

Republic of Hawaii: The Republic of Hawaiʻ i was the formal name of the nation of Hawaiʻ i between July 4, 1894, when the Provisional Government of Hawaii ended, and August 12, 1898, when it was annexed by the United States as a territory of the United States.  The Territory of Hawaii was formally established as part of the U.S. on June 14, 1900.

Supporting paragraphs: Peter Cushman Jones Republic of Hawaii
Answer: The Republic of Hawaiʻ