First you have to be recognized as the first one to have detected it from among all of the hundreds of people around the world every day that are themselves searching for the approximately 10 - 12 comets seen every year. You then send your discovery telegram to Dr. Brian Marsden at the Harvard/ Smithsonian Center for Astrophysics who is the appointed contact person selected by the International Astronomical Union to register these things. The comet will then be named after you, and any other co-discoverer of the earliest sighting. You cannot simply request that a comet be named after you. You have to be the first one, or among the first three, to have reported it to Marsden.