Some of the earliest recorded observations ever made through a telescope, Galileo's drawings on 28 December 1612 and 27 January 1613 contain plotted points that match up with what is now known to be the position of Neptune. On both occasions, Galileo seems to have mistaken Neptune for a fixed star when it appeared close—in conjunction—to Jupiter in the night sky; hence, he is not credited with Neptune's discovery. At his first observation in December 1612, Neptune was almost stationary in the sky because it had just turned retrograde that day. This apparent backward motion is created when Earth's orbit takes it past an outer planet. Because Neptune was only beginning its yearly retrograde cycle, the motion of the planet was far too slight to be detected with Galileo's small telescope. In July 2009, University of Melbourne physicist David Jamieson announced new evidence suggesting that Galileo was at least aware that the "star" he had observed had moved relative to the fixed stars.
In 1821, Alexis Bouvard published astronomical tables of the orbit of Neptune's neighbour Uranus. Subsequent observations revealed substantial deviations from the tables, leading Bouvard to hypothesise that an unknown body was perturbing the orbit through gravitational interaction. In 1843, John Couch Adams began work on the orbit of Uranus using the data he had. Via Cambridge Observatory director James Challis, he requested extra data from Sir George Airy, the Astronomer Royal, who supplied it in February 1844. Adams continued to work in 1845–46 and produced several different estimates of a new planet.
In 1845–46, Urbain Le Verrier, independently of Adams, developed his own calculations but aroused no enthusiasm in his compatriots. In June 1846, upon seeing Le Verrier's first published estimate of the planet's longitude and its similarity to Adams's estimate, Airy persuaded Challis to search for the planet. Challis vainly scoured the sky throughout August and September.
Meanwhile, Le Verrier by letter urged Berlin Observatory astronomer Johann Gottfried Galle to search with the observatory's refractor. Heinrich d'Arrest, a student at the observatory, suggested to Galle that they could compare a recently drawn chart of the sky in the region of Le Verrier's predicted location with the current sky to seek the displacement characteristic of a planet, as opposed to a fixed star. On the evening of 23 September 1846, the day Galle received the letter, he discovered Neptune within 1° of where Le Verrier had predicted it to be, about 12° from Adams' prediction. Challis later realised that he had observed the planet twice, on 4 and 12 August, but did not recognise it as a planet because he lacked an up-to-date star map and was distracted by his concurrent work on comet observations.
In the wake of the discovery, there was much nationalistic rivalry between the French and the British over who deserved credit for the discovery. Eventually, an international consensus emerged that both Le Verrier and Adams jointly deserved credit. Since 1966, Dennis Rawlins has questioned the credibility of Adams's claim to co-discovery, and the issue was re-evaluated by historians with the return in 1998 of the "Neptune papers" (historical documents) to the Royal Observatory, Greenwich. After reviewing the documents, they suggest that "Adams does not deserve equal credit with Le Verrier for the discovery of Neptune. That credit belongs only to the person who succeeded both in predicting the planet's place and in convincing astronomers to search for it."
Shortly after its discovery, Neptune was referred to simply as "the planet exterior to Uranus" or as "Le Verrier's planet". The first suggestion for a name came from Galle, who proposed the name Janus. In England, Challis put forward the name Oceanus.
Claiming the right to name his discovery, Le Verrier quickly proposed the name Neptune for this new planet, though falsely stating that this had been officially approved by the French Bureau des Longitudes. In October, he sought to name the planet Le Verrier, after himself, and he had loyal support in this from the observatory director, François Arago. This suggestion met with stiff resistance outside France. French almanacs quickly reintroduced the name Herschel for Uranus, after that planet's discoverer Sir William Herschel, and Leverrier for the new planet.
Struve came out in favour of the name Neptune on 29 December 1846, to the Saint Petersburg Academy of Sciences. Soon, Neptune became the internationally accepted name. In Roman mythology, Neptune was the god of the sea, identified with the Greek Poseidon. The demand for a mythological name seemed to be in keeping with the nomenclature of the other planets, all of which, except for Earth, were named for deities in Greek and Roman mythology.
Most languages today, even in countries that have no direct link to Greco-Roman culture, use some variant of the name "Neptune" for the planet. However, in Chinese, Japanese, and Korean, the planet's name was translated as "sea king star" (海王星), because Neptune was the god of the sea. In Mongolian, Neptune is called Dalain Van (Далайн ван), reflecting its namesake god's role as the ruler of the sea. In modern Greek the planet is called Poseidon (Ποσειδώνας, Poseidonas), the Greek counterpart of Neptune. In Hebrew, "Rahab" (רהב), from a Biblical sea monster mentioned in the Book of Psalms, was selected in a vote managed by the Academy of the Hebrew Language in 2009 as the official name for the planet, even though the existing Latin term "Neptun" (נפטון) is commonly used. In Māori, the planet is called Tangaroa, named after the Māori god of the sea. In Nahuatl, the planet is called Tlāloccītlalli, named after the rain god Tlāloc. In Thai, Neptune is referred both by its Westernised name Dao Nepjun (ดาวเนปจูน), and is also named Dao Ketu (ดาวเกตุ, "Star of Ketu"), after the descending lunar node Ketu (केतु) who plays a role in Hindu astrology.
From its discovery in 1846 until the subsequent discovery of Pluto in 1930, Neptune was the farthest known planet. When Pluto was discovered, it was considered a planet, and Neptune thus became the second-farthest known planet, except for a 20-year period between 1979 and 1999 when Pluto's elliptical orbit brought it closer than Neptune to the Sun. The discovery of the Kuiper belt in 1992 led many astronomers to debate whether Pluto should be considered a planet or as part of the Kuiper belt. In 2006, the International Astronomical Union defined the word "planet" for the first time, reclassifying Pluto as a "dwarf planet" and making Neptune once again the outermost known planet in the Solar System.