Question: What was the informal name of the company that captured the HMS Admiral Rainier more than once?

Context paragraphs:
HMS Hindostan (1804): HMS "Hindostan" (variously "Hindustan" or "Hindoostan") was a 50-gun two-decker fourth rate of the Royal Navy.  She was originally a teak-built East Indiaman named "Admiral Rainier" launched at Calcutta in 1799 that the Royal Navy brought into service in May 1804.  Before the Royal Navy purchased her, "Admiral Rainier" made two trips to England for the British British East India Company (EIC), as an "extra ship", i.e., under charter.  Perhaps her best known voyage was her trip to Australia in 1809 when she and "Dromedary" brought Governor Lachlan Macquarie to replace Governor William Bligh after the Rum Rebellion.  In later years she became a store ship, and in 1819 was renamed "Dolphin".  She was hulked in 1824 to serve as a prison ship, and renamed "Justitia" in 1831.  She was finally sold in 1855.

Koreanosaurus (theropod): "Koreanosaurus" (meaning "Korean lizard") is the informal name given to an as-yet undescribed genus of dinosaur from the Late Cretaceous.  It was a possible dromaeosaur (or similar theropod) which lived in what is now Korea, although at times it has been referred to the Tyrannosauridae and Hypsilophodontidae.  Based solely on a femur, the type species was coined by Kim in 1979, who by 1993 had decided that it was a species of "Deinonychus", and created the informal name "D." "koreanensis".  It is probably the same as "Koreasaurus", another informal name for a possible Korean dromaeosaurid.

Hexachlorocyclohexa-2,5-dien-1-one: Hexachlorocyclohexa-2,5-dien-1-one, sometimes informally called hexachlorophenol (HCP) is an organochlorine compound.  It can be prepared from phenol.  Despite the informal name, the compound is not a phenol but is a ketone.  The informal name is derived from its method of preparation which includes phenol as a reagent.

John Tremayne Rodd: Little is known of Rodd's early life, but during the French Revolutionary Wars he served as a commander in the sloops HMS "Bonetta" and HMS "Scorpion" .  In the former he participated in the capture of the French privateer "Le Poisson Volant" in the West Indies on 4 August 1796, and in the latter he captured the Dutch privateer "Courier", for which was promoted to post captain on 7 September 1798.  After the Peace of Amiens in 1803, Rodd briefly took command of the first rate ship of the line  under Admiral Sir Charles Cotton, but by 1805 had moved to the veteran frigate HMS "Indefatigable" .  In "Indefatigable", Rodd served as the main scout for the British squadron blockading Brest, France.  In 1805 he sighted the French fleet under Admiral Ganteaume attempting to escape and warned the Offshore Squadron, who drove the French back into Brest in a brief engagement.  In 1806, Rodd was working in conjunction with Captain Lord Cochrane in HMS "Pallas" and on 15 July "Indefatigable" was the launch point for a fleet of small boats that attacked a French convoy in the Gironde.

Penny: A penny is a coin ( pennies) or a unit of currency ( pence) in various countries.  Borrowed from the Carolingian denarius (whence its former abbreviation d.), it is usually the smallest denomination within a currency system.  Presently, it is the formal name of the British penny ( p) and the informal name of one American cent (.  ¢) as well as the informal Irish designation of 1 cent euro coin (.  c).  It is the informal name of the cent unit of account in Canada, although one cent coins are no longer minted there.  The name is also used in reference to various historical currencies also derived from the Carolingian system, such as the French denier and the German pfennig.  It may also be informally used to refer to any similar smallest-denomination coin, such as the euro cent or Chinese fen.

Informal hall: At traditional Oxbridge and many Durham colleges, there may be two dinners in the college hall each evening, named informal hall and formal hall.  Informal hall normally takes place before formal hall and does not require the wearing of a gown.  It is typically self-service rather than being served by college servants.  It is also relatively early in the evening, thus allowing students to pursue other activities later.  In some colleges, this leads to its alternative name of first hall.  Often the meal is also known by an informal name, such as Buttery, Trough, or just the Canteen.

HMS Admiral Rainier (1800): HMS "Admiral Rainier" was a Dutch 16-gun brig that the British captured on 23 August 1800 at Kuyper's Island, Java.  They took her into service and named her after Admiral Peter Rainier, the leader of the British expedition.  After the British sold her in 1803 apparently the French captured her in 1804 and sold her to the Dutch colonial government in Batavia for anti-piracy patrol.  Her Javanese crew mutinied in 1806 and eventually sailed to Penang where vessels of the British East India Company (EIC) seized the vessel.  She returned to British service, only to be captured and recaptured by vessels of the EIC.  Her ultimate fate is unknown.

East India Company: The East India Company (EIC), also known as the Honourable East India Company (HEIC) or the British East India Company and informally as John Company, was an English and later British joint-stock company, which was formed to pursue trade with the "East Indies" (in present-day terms, Maritime Southeast Asia), but ended up trading mainly with Qing China and seizing control of the Indian subcontinent.

Fried Egg structure: The Fried Egg is an informal name for an underwater geomorphic structure located in the North Atlantic that is a suspected impact crater.  This structure lies at a depth of 2 km and is about 150 km from the Azores archipelago.  It consists of a dome 300 m high and 3 km in diameter that lies within a larger and roughly circular depression 110 m deep and 6 km in diameter.  It is this morphology on which its informal name is based.  Images that accompany media reports show the presence of a well-defined rim that surrounds the depression.  These images also show a second but smaller circular depression, which also has a central peak, lying adjacent to the Fried Egg structure.

HMS Renard (1803): HMS "Renard" was a 12-gun schooner, previously the French navy schooner "Renard".  HMS "Cameleon" captured her in 1803 off Corsica and the Royal Navy took her into service under her existing name.  The already being an HMS "Renard" (a sloop), on the West Indies station, at some point between 1804 and 1807 the schooner's name was changed to HMS "Crafty".  During her brief service "Renard"/"Crafty" captured several merchantmen and a small armed vessel.  In 1807 three Spanish privateers captured her.

Supporting paragraphs: HMS Admiral Rainier (1800) East India Company
Answer: John Company