To add a user, you'll enter the user's First name and Last name, and this will assemble the Display name by default. If you want the display name to be something different than the first and last names, change it after it populates by default; this won't affect the first or last names:
Most instances of Office 365 have more than one domain, but usually, one's the real domain, and one's domain.onmicrosoft.com, which hardly anyone uses. In most Office 365 tenants, the default domain has been set to whatever your company usually uses for public websites and the like. However, there might be circumstances where a user ...