The Milky Way galaxy contains between 100 billion and 400 billion stars. There is only a tiny fraction of those stars can be named, of course, which is why names are generally only assigned to stars that stand out for some reason as being exceptional.
Brightness is one metric by which stars can stand out. Stars' brightness, as seen from Earth, depends on their absolute magnitude and their distance from the Earth. Apart from the Sun, Sirius is the brightest star presently visible from the Earth. Canopus, Rigel Kentaurus, Arcturus and Vega make up the rest of the top five, according to About.com.
According to Wikipedia, most star names derive from Latin or Arabic. Many stars are known by their location and apparent magnitude relative to their parent constellations. Hence, Epsilon Eridanus is the fifth-brightest star in the constellation of the snake, while Alpha Centauri is the most luminous member of the Centaurus constellation.
Theer are some stars that are assigned the names of their discoverers. Such is the case with Barnard's Star, which is named in honor of Edward Emerson Barnard, who first discovered it in 1916 and who was the first to describe the star's large relative motion.