Bayer system of Naming Stars
courtesy of U.S. Naval
The Uranometria contains 51 star charts: one for each of Ptolemy's 48 constellations, one including 12 new southern constellations devised by Dutch explorers Pieter Dircksen Keyzer and Frederick de Houtman, and then two charts showing the entire northern and southern hemispheres of the sky.
Bayer grouped the stars in each constellation by brightness or magnitude, then assigned them a lower case Greek letter from alpha (α) to omega (ω). After using these 24 letters, he used the lower case Roman letter, skipping j and v since in Roman writing they can be confused with i and u.
Thus the Bayer designation for the brightest star in the constelllation Centaurus would be alpha Centauri (Centauri being the Latin genitive form of Centaurus). Stars that were close together and close and magnitude were given the same designation. For example, Bayer listed the 6 stars in Orion's "pelt" as pi Orionis. These were relabeled as π1- π6 Orionis by subsequent astronomers.
If you are interested you can find any of the modern constellation names with Latin nominative and genitive forms on my constellation list.