You want those shares in your name if things pop off. There's a lot of re-hypothecated synthetic shares rolling around. It also prevents them from being loaned out by your broker.

Fidelity is probably the easiest to perform the drs transfer. Login and go to their live chat, 7se the automated assistant. Type Direct Register and you'll see the correct option.

From there in a few days you'll register with computershare.com which holds your shares for gamestop. Gamestop uses them as official record keeper. They also send paper mail to u a few weeks after Fidelity moves the shares.

Drsgme.org has step by step instructions that may differ slightly