At the center of the Milky Way, we have a supermassive black hole. It's name is "Sagittarius A*". I was wondering that why is it called so? I mean, why "A*" why not just "A". Is there a naming system for super massive black holes?
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The short answer is that, as George notes in his answer, there is no naming system for supermassive black holes. I wouldn't say they're really "named" after their host galaxies; more that when one wants to refer one, you usually do it by using the name of the galaxy (e.g., "the SMBH in M31" or "M87's SMBH").
"Sgr A*" is actually the name of a radio source, a subcomponent of the radio source Sgr A which happens to be associated with the Galaxy's SMBH.
The very early system for naming radio sources -- before better radio telescopes found so many that the system became unworkable -- was basically "name of constellation" + "decreasing brightness rank". So Sgr A was simply the brightest radio source in the constellation of Sagittarius. (In fact, the system was abandoned before most constellations even got to B.) Most such sources are not black holes; for example, Casiopeia A is a supernova remnant, as is Taurus A (the Crab Nebula).
Check this wiki link out. "The name Sgr A* was coined by Brown in a 1982 paper because the radio source was "exciting", and excited states of atoms are denoted with asterisks."
There is no unified naming system for black holes. They are usually named after their host galaxy. Others are identified by the name of the survey in which they were observed. A few black holes are catalogued by their constellation and the order in which they were discovered
EDIT: The 1982 paper by Brown and Lo can be found here.