To add your Discord username to your Gamepedia Profile, navigate to your profile by going to the top right menu (with your username) and clicking My user Page.
On the profile page, there will be several pen icons, meaning Edit.
Click the one second from the bottom.
This screen will allow you to add various social, gaming, and other usernames to your profile.
Add your Discord username with the # and numbers (the discriminator) to the Discord field and hit save.