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Designations of stars (and other celestial bodies) is done by the International Astronomical Union (IAU). Many of the star names in use today were inherited from the time before the IAU existed. Other names, mainly for variable stars (including novae and supernovae), are being added all the time.
Approximately 10,000 stars are visible to the naked eye. Pre-modern catalogues listed only the brightest of these. Hipparchus in the 2nd century BC enumerated about 850 stars. Johann Bayer in 1603 listed about twice this number. Only a minority of these have proper names, all others are designated by catalogization schemes. Only in the 19th century did star catalogues list the naked-eye stars exhaustively. The most voluminous modern catalogues list of the order of a billion stars, out of an estimated total of 200 to 400 billion in the Milky Way.
Proper names 
There are a number of problems with these names, however:
- Spellings are often not standardized (Almach or Almaach or Almak or Alamak)
- Many stars have more than one name of roughly equal popularity (Mirfak or Algenib or Alcheb; Regor or Suhail al Muhlif; Alkaid or Benetnasch; Gemma or Alphecca; Alpheratz and Sirrah)
- Because of imprecision in old star catalogs, it may not be clear exactly which star within a constellation a particular name corresponds to (e.g., Alniyat can refer to Sigma Scorpii or Tau Scorpii, Chara).
- Some stars in entirely different constellations may have the same name: Algenib in Perseus and Algenib in Pegasus; Gienah in Cygnus and Gienah in Corvus, Alnair in Grus and Alnair in Centaurus.
In practice, the traditional names are only universally used for the very brightest stars (Sirius, Arcturus, Vega, etc.) and for a small number of slightly less bright but "interesting" stars (Algol, Polaris, Mira, etc.). For other naked eye stars, the Bayer designation is often preferred.
In addition to the traditional names, a small number of stars that are "interesting" can have modern English names. For instance Barnard's star has the highest known proper motion of any star and is thus notable even though it is far too faint to be seen with the naked eye. See stars named after people.
Two second-magnitude stars, Alpha Pavonis and Epsilon Carinae, were assigned the proper names Peacock and Avior respectively in 1937 by Her Majesty's Nautical Almanac Office during the creation of The Air Almanac, a navigational almanac for the Royal Air Force. Of the fifty-seven stars included in the new almanac, these two had no classical names. The RAF insisted that all of the stars must have names, so new names were invented for them.
- It lists many Assyrian/Babylonian and Sumerian star names recovered by archaeology, and some of these (e.g. Sargas and Nunki) have come into general use.
- It lists many Chinese star names (e.g. Cih alias Tsih), though these have not come into general usage.
- R.H.Allen represented the "kh" sound by 'h' with a dot above (ḣ), and at least one astronomy book (a book by Patrick Moore) using R.H.Allen as a source, has misread this unfamiliar letter as 'li'.
A few stars are named for individuals. These are mostly unofficial names that became official at some juncture. The first such case (discounting characters from Greek mythology) was Cor Caroli (α CVn), named in the 17th century for Charles I of England. The remaining examples are mostly stars named after astronomers or astronauts.
Catalogue numbers 
In the absence of any better means of designating a star, catalogue numbers are generally used. A great many different star catalogues are used for this purpose, see star catalogues.
By constellation 
The first modern schemes for designating stars systematically labelled them within their constellation.
- The Bayer designation is such a system, published by Johann Bayer in 1603. It introduced a system of designating the brightest stars in each constellation by means of Greek (or less often Latin) letters, and is still widely used. The original list of Bayer designations contained 1,564 naked-eye stars.
- The Flamsteed designation uses the same approach, using numbers rather than letters. Published in 1712 (without the consent of the author, John Flamsteed), it lists 2,554 stars.
- The Gould designation by Benjamin Gould (1879) also lists stars by constellation, but numbers them by increasing order of right ascension.
- Hevelius and Bode both numbered stars within constellations similarly. Their number systems has fallen out of use, but their designations even now are occasionally mistakenly treated as Flamsteed designations. 47 Tucanae, a number assigned by Bode, is a famous example.
Full-sky catalogues 
Full-sky star catalogues detach the star designation from the star's constellation and aim at enumerating all stars with apparent magnitude greater than a given value.
- the Histoire Céleste Française (1801) enumerated 47,390 stars to magnitude 9.
- the Bonner Durchmusterung (1859) was the most complete star catalogue compiled without the aid of photography. It listed a total of 320,000 northern stars, expanded by the Cordoba Durchmusterung (1892) and the Cape Photographic Durchmusterung (1896).
- the Henry Draper Catalogue (1924) listed 225,300 stars to magnitude 10, extended to a total of 359,083 in 1949. The HD numbers remain in widespread use for stars that do not have a Flamsteed or Bayer designation.
- the Bright Star Catalogue of 1930 listed all stars brighter than magnitude 6. It was supplemented to include stars down to magnitude 7.1 in 1983.
- the Catalogue astrographique was compiled between 1891 and 1950 with the aim of listing all stars to magnitude 11, resulting in a list of 4.6 million stars. It is under continued development, now under custody of the U.S. Naval Observatory.
- the USNO-B1.0 catalogue contains over a billion objects, and is also under continued development at the U.S. Naval Observatory.
- the online Guide Star Catalog II (2008) contains 945 million stars to magnitude 21.
Variable designations 
Variable stars which do not have Bayer designations are given special designations which mark them out as variable stars.
Exoplanet searches 
When a planet is detected around a star, the star is often given a name and number based on the name of the telescope or survey mission that discovered it and based on how many planets have already been discovered by that mission e.g. HAT-P-9, WASP-1, COROT-1, Kepler-4.
Sale of star names 
There are a number of companies that sell naming rights to obscure stars for commemorative purposes. These sales of star names are not recognised by astronomers, nor by any international scientific or registration body. As a result a single star can potentially be named independently by multiple companies, or multiple times by the same company.
See also 
- Under average conditions, about 5,600 stars brighter than +6m are visible to the naked eye; theoretically, under perfect conditions, about 45,000 stars brighter than +8m would be visible.
- The NASA in 1971 compiled a "technical memorandum" collecting a total of 537 named stars. Technical Memorandum 33-507 – A Reduced Star Catalog Containing 537 Named Stars, NASA-CR-124573 (1971).
- Sadler, Donald. "A Personal History of H.M. Nautical Almanac Office". Retrieved 2010-09-26.
- Star Names: Their Lore and Meaning by R.H.Allen (ISBN 0-486-21079-0) free version here
- IAU: "Buying Stars and Star Names"
- List of popular star names
- The Naming of Stars from the National Maritime Museum
- The Straight Dope: Can you pay $35 to get a star named after you?
- Naming Stars