Star Names and the Greek Alphabet
Many stars have many different names, coming from many different naming systems. For instance, the red giant star Betelgeuse is also known as Alpha Orinis.
This article at Sky & Telescope's web site has an extensive discussion of the various names for stars you will see (including why those "buy the name of a star" outfits are bogus). Many of the brightest stars have Bayer designations, originally given to them in the 17th century by Johann Bayer. These designations start with a greek letter, followed by the name of a constellation (in possessive form). Usually, the brighest star is alpha, and dimmer stars work down through the Greek alphabet from there. So, Vega, the brighest star of the constellation Lyra, is also known as Alpha Lyrae.
So that you can compare a star chart with names spoken out loud for stars, it is useful to know the Greek alphabet: