Q: I have multiple users on my Mac and I was wondering how you tell the system to retain all the user names so they don't have to enter their email addresses every time ???

Email addresses into what?

Each user should have their own account and password to log in.  Each is independent of the other.  So for Mail each has their own Mail account if they set one up in Mail. 

That's the way it should be set up.  Are you using a single account and allowing multiple users to use that one single account?  If so then in Mail at least you could set up individual mail accounts.  But everything else in the system is shared.