Stars within a given constellation are usually ranked according to relative brightness by the Greek alphabet. The brightest star is alpha, the second-brightest beta, the third-brightest gamma, and so forth. There are some exceptions, when an especially common constellation (such as Ursa Major or Crux) is numbered according to its linear sequence, like a dot-to-dot diagram.
Star names have two parts; the first is the Greek letter indicating its brightness. The second part of a star name indicates its constellation. To obtain this constellation part of the star name, the letter of the Greek alphabet which indicates a star's brightness is conjoined with the Latin genitive case of the name of the constellation. For example, the brightest star of the constellation Centaurus is "alpha-Centauri," which happens to be the star nearest to our own Sun (though it is actually a multiple star system). "Centauri" is the Latin genitive case of "Centaurus." In general, the genitive case is obtained by changing the suffix "-us" to "-i," (e.g., Taurus becomes Tauri). Or, for constellations not ending in "-us," add "-is" (e.g., Orion becomes Orionis). For your convenience, the genitive case is indicated at the top of the web page for each constellation.