How can I use my epicgames name as an ingame name?

I recently created an epic account, I didn't have one before and I played fortnite just like that (approx. 2 years). Now I have created the epic account and everything worked, it is also displayed when you go to a profile, but it is not used for e.g. B. Displayed on kill messages, but my xbox name. I wanted to ask how it works that the epic name is displayed on the console.

EpicGames does not work on xbox / ps4.

OK thank you