Hi,
if nothing made sense of what you already read, i doubt i can help you as i would certainly repeat the same things… 😉
Nickname doesn’t exist in WordPress. On a WP install, a new user is only asked for a username(generally it’s a nickname like creatorsite), an email and a password. That’s all!
By convinience, a WP user can add his first and last name to his profile, but it is not an obligation.
When BP is added, he adds a mandatory field called Name which can by filled with first and last name or whatever else. Only the field is mandatory, not the content. And you can change his nale to what you want. Eg. Your dogs name. An other difference for this field is that it let you enter uppercase and space, what the WP username field doesn’t allow. BP use this field to synchronize members from WP and those registered once BP is activated.
Users are handled by WP, not by BP which is only a plugin, btw. both use the same DB user table.
Here a complete description of WP’s database, and read attentively the part related to wp_users.
Nickname = username. Your question is related to username vs. display_name.
Read here for a solution.
ps: your picture mention that nicknames can eliminate a security issue. Which one exactly ? i’m curious to learn how over 200 000 active BP sites are threatened by hackers seaking for usernames in 2016 !