BuddyPress.org

@aboutm2 please paste this code snippet and check it as per your requirement.

// Hide user name from BuddyPress profile
function hide_user_name_from_profile() {
    if ( bp_is_active('xprofile') ) {
       ?>
		<style>
			.user-nicename{
				display:none;
			}
		</style>
	<?php
    }
}
add_action( 'wp', 'hide_user_name_from_profile');