Every star astronomy deals with has its own name and category. This process can be almost as confusing and complex as astronomy itself.
Thanks to telescopes, we are now able to see over a million stars. However, there is many a star astronomy has not even bothered to give a name. Unless it is an unusual or rare type of star astronomy officials would not even recognize it. This makes a certain amount of sense, especially to a person given the task of naming all of these stars! This is also an indication that many of the companies that offer you the chance to "name your own star" in exchange for money are in fact scams. There are certain guidelines that come with naming stars and many of the companies that offer these opportunities in exchange for money should be researched before being contacted for such an opportunity. Each star astronomy experts find must be catalogued in a very specific way.
The process of naming stars is actually rather dull. Stars are first classified by how bright they are. These brightness levels use the Greek alphabet as their scale. Alpha is the brightest, and so on. After these letters run out, we switch to lower-case letters of the ROMAN alphabet! While this creates generic, uninteresting names like Vega 3 Lyrae, it is ultimately necessary to make star names so boring. With so many stars, it would be nearly impossible to come up with creative and interesting names for each one. This unfortunately makes it a bit less wondrous and exciting to look into a telescope, see a beautiful and shining celestial body, and find out that its names is M113Vega. This is the nature of star astronomy, however.
Any star astronomy has not given a name is probably not visible with the naked eye. It most certainly is not a part of any constellation, either, because these stars took priority when it came to being given names. Many of these stars, in fact, have had several different names assigned to them over the entire span of civilization. Ancient cultures from Greece to America to Egypt have been fascinated by the same stars that fascinate us today, and each culture came up with names for the stars and constellations. Many of these cultures formed entire religions based around the night sky and created not just names but epic stories about these sky creatures that live on even today. There was, understandably, a notable drop-off of this activity after telescopes were invented. In some ways it seems that technology has taken a bit of the wonder and spirit out of our fascination with the night sky.