I have already done these steps multiple times. If you read my initial message, the issue is only happening in the App. When I send emails in the app the recipient (and me!) see my email address as my display name followed by my email address even though my display name is my first name and my surname.
I have tried changing my display name to a nickname plus surname but same happens: it displays my email address as my display name. I think there is a glitch in the app that you need to sort and consequently, Licquorice's advice seems very sound!