Your Epic Games display name is the name that appears on your account on the Epic Games Launcher, their official forum, AnswerHub, and in-game.
Follow Epic Games' steps to change your Epic Games display name.
Your email address must be verified before you can change your name. Here's how to verify your email if you haven't already done so.
FYI: This will not change your in-game name on RuneScape or Old School RuneScape.