"Lift your eyes and look to the heavens: Who created all these?
He who brings out the starry host one by one, and calls them each by name.
Because of his great power and mighty strength, not one of them is missing."
Stars within a given constellation are usually ranked according to relative brightness ("apparent magnitude") 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.