Hi,
Those popular names for stars are mostly derived from the Arabic (Muhlifain), Latin (Capella), Greek and other languages. Not every star has a well-known popular name.
The designations beginning with a letter from the Greek alphabet are called Bayer designations, and are often given in order of apparent magnitude starting with Alpha for the brightest.
However this is confusing because there are about 30 constellations in which Alpha is not the brightest star !
It gets more tangled still when the Greek alphabet runs out of letters in a constellation.
http://www.ianridpath.com/starnames.htm
http://www.naic.edu/~gibson/starnames/starnames.html
http://en.wikipedia.org/wiki/Bayer_designation
Cheers