The company that keeps the registered shares for GameStop is Computershare, they also keep registered shares for Apple and many other companies. Other stocks may use other companies. Anyway, all you have to do is tell your broker you want them to be directly registered and they have to do it. Fidelity and some other decent brokers do it for free. If your broker wants to charge you to do it, perhaps, you should look for another broker. Your broker transfers them and opens an account in your name with Computershare.