If you are the first to report the comet to the official bureau at the Smithsonian Astrophysical Observatory run by Dr. Brian Marsden, and can provide detailed coordinates, then you are first in line for getting the comet named after yourself. This is the only way that comets are named, buy their discoverers. If more than one discoverer exists because they observed the comet an got their telegram to Brian Marsden at the same time, then the Comet gets two or more names. As for stars, only astronomers who study stars get to name them if the star is not already in a catalog. Sometimes astronomers observing at different wavelengths will identify stellar objects by some name they decide upon. In rare instances, astronomers discover new clusters or galaxies and are allowed by the International Astronomical Union to name them after themselves such as 'Maffei I' or 'Liller 1'. Most of the time, however, an astronomer just publishes a catalog of objects and names them 'FIR-1', 'FIR-2' etc or some other name.