Ok, you this CSS too:
#wpforo-wrap .wpforo-members-content .wpf-members-info .wpf-author-nicename{display: none;}
In this forum, the people with first name and last name, but I do not want that the public are not displayed, only self-selected nicknames should be displayed there, is that feasible?
That's not First and Last name, that's Display Name. They can change their Display Names in My Profile > Account page. Display Names are designed to be displayed. This is the WordPress and wpForo logic. Nicknames are used in URL and on @mentioning.