There is no place where you can purchase a star. There are a few businesses which claim to sell or name stars, but the names they give are not recognized by anyone in the scientific community. Stars are named by the International Astronomical Union, headquartered in Paris, France. They are given numbers determined by their exact location in the sky. This system is organized so that it is most beneficial to the scientists who are studying them. Occasionally a comet or other solar system object is named after people, often by or after the person who discovered it, but stars are not. If you do locate a company trying to sell you a star, know that the star they "sell" you will never be known as your star by anyone but you. There is nothing stopping them from "selling" the same star over and over again. Here is the general policy that the IAU has for naming all other objects in the sky.