That screenshot is the Microsoft Edge profile menu. The email address is being shown because that Microsoft account is connected to the Edge profile.
Unfortunately, Edge does not have a setting to hide or mask just the email address while keeping that profile signed in. The address is used to identify which account/profile Edge is using.
If you do not want the address to appear there, the practical option is:
Edge > Profile icon > Profile settings > Sign out
Or remove that Edge profile completely. Be aware that signing out stops synchronization of favorites, passwords, history, etc.
https://support.microsoft.com/edge/sign-in-and-create-multiple-profiles-in-microsoft-edge