I'm not sure how you woudl get them to login via an email address, but you CAN change what is displayed across the site via the template. If they fill in their profile info with First & Last names, and you edit the templates to use this, that'll do it.
But that's not what I'm asking! Aarrgghh!!
I really try to be nice and patient on the Wordpress forum, but everytime time I ask something that goes just a little bit outside default Wordpress, I get these off-topic answers explaining how Wordpress does things.
Sign-up/log-in with just email address and password is not that unusual. It happens all over the web.
I just was mentioning what the previous discussions on the topic boiled down to.
Those discussions were similarly led off track then. Or were not about this topic in the first place.
Again, the goal:
Eliminate the concept of the "username", because it's too anonymous and gives members one more thing they have to remember.
Allow members to register/login with just their email address + password. If they forget their password, they can retrieve it by email address.
Of course (!) the email address should NEVER be displayed in the site instead of a username. For display the real name, first and/or last, should be used.
How could I approach this? Which files should I focus on?
I've started a blunt-force approach; replace user_login with user_email, see what happens and what I have to clean up. I'll report back on any progress...