You’re not permitted to use the Epic trademarks without a trademark license from Epic and that is not included in the EULA. The EULA prevents you from causing confusion with Epic’s trademarks, such as naming your product in a way that implies it comes from Epic or using Epic logos to imply your product is official.
There is a trademark license, but the license would not permit naming your product as you have suggested or using the UE4 logo as the imagery for the app.
Have you considered trying to sell it on the UE4 Marketplace?