While using the common naming system does work, eventually astronomers will run out of names when they exhaust the world’s mythological deities, creatures, and more. In about 1603 astronomers developed a systemic naming convention to use instead, called the Bayer Naming System.
With this system, the brightest stars in the sky and in their individual constellations are given a name that includes the Latin possessive name of the constellation and a Greek letter of designation. This naming convention is approximate, as some stars which carry a Greek letter further down the alphabet may be brighter than the ones named before it. So let us consider Betelgeuse. It is known in the Bayer system as Alpha Orionis with Rigel being Beta Orionis. If we break this down and look at the parts it reads as follows:
Common name: Betelgeuse
Constellation: Orion
Latin Possessive: Orionis
Bayer name: Alpha Orionis (Alpha is the first letter of the Greek alphabet)