Since I really only run 1 domain, is there a way that I can make is so my users just have to type in their name and not full email address?
Definitely:
there is an option in the toaster-watcher.conf:
vpopmail_default_domain = 0
change 0 to your domain, exampe.com or whatever your domian is.
I'm moderately sure you'd have to recompile vpopmail after making that change.
You'd have to run
toaster_setup.pl -s vpopmail