Only a tiny minority of known stars have proper names; all others have only designations from various catalogues or lists, or no identifier at all. Hipparchus in the 2nd century BC enumerated about 850 naked-eye stars. Johann Bayer in 1603 listed about twice this number. Only in the 19th century did star catalogues list the naked-eye stars exhaustively. The Bright Star Catalogue, which is a star catalogue listing all stars of apparent magnitude 6.5 or brighter, or roughly every star visible to the naked eye from Earth, contains 9,096 stars. The most voluminous modern catalogues list on the order of a billion stars, out of an estimated total of 200 to 400 billion in the Milky Way.
Proper names may be historical, often transliterated from Arabic or Chinese names. Such transliterations can vary so there may be multiple spellings. A smaller number of names have been introduced since the Middle Ages, and a few in modern times as nicknames have come into popular use, for example Sualocin for α Delphini and Navi for γ Cassiopeiae.
The International Astronomical Union (IAU) has begun a process to select and formalise unique proper names for the brighter naked-eye stars and for other stars of popular interest. To the IAU, name refers to the (usually colloquial) term used for a star in everyday speech, while "designation is solely alphanumerical" and used almost exclusively in official catalogues and for professional astronomy. Many of the names and some of the designations in use today were inherited from the time before the IAU existed. Other designations are being added all the time. As of the start of 2019, the IAU had decided on a little over 300 proper names, mostly for the brighter naked-eye stars.
In 2016, the IAU organized a Working Group on Star Names (WGSN) to catalog and standardize proper names for stars. The WGSN's first bulletin dated July 2016 included a table of 125 stars comprising the first two batches of names approved by the WGSN (on 30 June and 20 July 2016) together with names of stars (including four traditional star names: Ain, Edasich, Errai and Fomalhaut) reviewed and adopted by the IAU Executive Committee Working Group on Public Naming of Planets and Planetary Satellites during the 2015 NameExoWorlds campaign and recognized by the WGSN. Further batches of names were approved on 21 August, 12 September, 5 October and 6 November 2016. These were listed in a table of 102 stars included in the WGSN's second bulletin dated November 2016. The next additions were done on 1 February 2017 (13 new star names), 30 June 2017 (29), 5 September 2017 (41), 17 November 2017 (3) and 1 June 2018 (17). All 330 names are included in the current List of IAU-approved Star Names, last updated on 1 June 2018 (with a minor correction posted on 11 June 2018).
In practice, 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 or Flamsteed 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, 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 traditional names. The RAF insisted that all of the stars must have names, so new names were invented for them. These names have been approved by the IAU WGSN.
A few stars are named for individuals. These are mostly names in common use that were taken up by the scientific community at some juncture. The first such case (discounting characters from mythology) was Cor Caroli (α CVn), named in the 17th century for Charles I of England. The remaining examples are mostly named after astronomers, the best known are probably Barnard's Star (which 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), Kapteyn's Star and recently Tabby's Star.
The International Astronomical Union has held two NameExoWorlds contests to give proper names to exoplanets and their host stars, in 2014/5 and 2019. As a result, several stars were named after people, including Cervantes for Mu Arae, Copernicus for 55 Cancri A, and Rosalíadecastro (HD 149143) after the writer Rosalía de Castro.
In the absence of any better means of designating a star, catalogue designations are generally used. Many star catalogues are used for this purpose; see star catalogues.
The first modern schemes for designating stars systematically labelled them within their constellation.
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 cut-off value.
Variable stars that do not have Bayer designations are assigned designations in a variable star scheme that superficially extends the Bayer scheme with uppercase Latin letters followed by constellation names, starting with single letters R to Z, and proceeding to pairs of letters. Such designations mark them as variable stars. Examples include R Cygni, RR Lyrae, and GN Andromedae. (Many variable stars also have designations in other catalogues.)
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, TRAPPIST-1.
Star naming rights are not available for sale via the IAU. Rather, star names are selected on a non-commercial basis by a small number of international organizations of astronomers, scientists, and registration bodies, who assign names consisting usually of a Greek letter followed by the star's constellation name, or less frequently based on their ancient traditional name.
However, there are a number of non-scientific "star-naming" companies that offer to assign personalized names to stars within their own private catalogs. These names are used only within that company (and usually available for viewing on their web site), and are not recognized by the astronomical community, or by competing star-naming companies. A survey conducted by amateur astronomers discovered that just over half of consumers would still want to "name a star" with a non-scientific star-naming company even though they have been warned or informed such naming is not recognized by the astronomical community.