Enforces the format of the BuddyPress Name field and WordPress Display Name field.

bp-enforce-display-name.php

<?php
/**
 * Plugin Name: BP Enforce Display Name
 * Description: Enforces the format of the BuddyPress Name field and WordPress Display Name field.
 * Plugin URI:  https://gist.github.com/christianwach/5f07b5cbc0b9067d2353e13cd19806be
 * Version:     1.0
 * Author:      Christian Wach
 * Author URI:  https://github.com/christianwach
 */

add_action( 'user_register', 'bpedn_update_display_name', 100, 1 );
add_action( 'profile_update', 'bpedn_update_display_name', 100, 1 );

/**
 * Update the WordPress User "Display Name" field.
 *
 * @since 1.0
 *
 * @param integer $user_id The numeric ID of the WordPress User.
 */
function bpedn_update_display_name( $user_id ) {

	// Bail if BuddyPress is not active.
	if ( ! function_exists( 'xprofile_set_field_data' ) ) {
		return;
	}

	// Get the User record.
	$user = new WP_User( $user_id );
	if ( ! $user->exists() ) {
		return;
	}

	/*
	 * Construct the "Display Name" the way BuddyPress used to.
	 *
	 * There are, of course, many options for this - so you may want to adapt
	 * this line of code to suit your own requirements.
	 */
	$full_name = $user->first_name . ' ' . $user->last_name;

	// Remove our callbacks.
	remove_action( 'user_register', 'bpedn_update_display_name', 100 );
	remove_action( 'profile_update', 'bpedn_update_display_name', 100 );

	// Build update args.
	$args = [
		'ID' => $user_id,
		'display_name' => $full_name,
	];

	// Update the WordPress User record.
	wp_update_user( $args );

	// Update BuddyPress "Name" field directly.
	xprofile_set_field_data(
		bp_xprofile_fullname_field_name(),
		$user_id,
		$full_name
	);

	// Reinstate our callbacks.
	add_action( 'user_register', 'bpedn_update_display_name', 100, 1 );
	add_action( 'profile_update', 'bpedn_update_display_name', 100, 1 );

}