Re: fullname vs username vs first + last name…
BuddyPress uses the “display name” to know that they have filled out some profile information. It is the only *always* required field inside BuddyPress.
Because WordPress is centered around the “username” and uses the “nicename” for slug purposes, we’re stuck with those no matter what. I like having my username be short for easy log ins if I can help it of course (sometimes “jjj” is already taken.), but I like my display name be my fullname because it’s how people recognize me.
I don’t see a way around this any time soon. And like Andy said, internationally sometimes people have 4 or more names. I use my middle name, but having a “middle name” field isn’t always optimal either so I lump it in with my first name. (All those years of my mom yelling “John James you get over here this instant!!” must have stuck with me.) 
You can rename the primary name field to be whatever you’d like, which is designed to alleviate some of the confusion. It lets you decide what that field means to your users. The “username” is the only thing they can’t change, so they’re using that for life. 
