Hides the default Name field on BuddyPress Registration form and Profile Edit screens.

bp-hide-name-field.php

<?php
/**
 * Plugin Name: BP Hide Name Field
 * Description: Hides the default Name field on BuddyPress Registration form and Profile Edit screens.
 * Plugin URI:  https://gist.github.com/christianwach/06d878edc277ce1ca8a7e59a82052744
 * Version:     1.1
 * Author:      Christian Wach
 * Author URI:  https://github.com/christianwach
 */

add_filter( 'bp_after_has_profile_parse_args', 'bphnf_intercept_profile_query_args' );

/**
 * Filters the xProfile query to hide the "Name" field on the Registration screen.
 *
 * Apply to registration form whichever page it is displayed on, whilst avoiding
 * splitting the Name field into First Name and Last Name fields in the profile
 * display loop of the User. Note that we cannot determine if we are in the loop
 * prior to the query, so we test for an empty User ID instead.
 *
 * @since 1.0
 *
 * @param array $args The existing arguments used to query for fields.
 * @return array $args The modified arguments used to query for fields.
 */
function bphnf_intercept_profile_query_args( $args ) {

	// User must be logged out.
	if ( is_user_logged_in() ) {
		return $args;
	}

	if ( ! bp_is_user_profile() OR ( bp_is_user_profile() AND empty( $args['user_id'] ) ) ) {

		// Query only group 1.
		$args['profile_group_id'] = 1;

		// Exclude name field (bp_xprofile_fullname_field_id is available since BP 2.0).
		$exclude_fields = bp_xprofile_fullname_field_id();

		// Merge with existing if populated.
		$args['exclude_fields'] = bphnf_merge_excluded_fields( $args['exclude_fields'], $exclude_fields );

	}

	return $args;

}

add_filter( 'bp_after_has_profile_parse_args', 'bphnf_intercept_profile_query_filter' );

/**
 * Filters the xProfile query to remove the "Name" field from the Profile Edit screen.
 *
 * @since 1.0
 *
 * @param array $args The existing arguments used to query for fields.
 * @return array $args The modified arguments used to query for fields.
 */
function bphnf_intercept_profile_query_filter( $args ) {

	// If on profile edit screen.
	if ( bp_is_user_profile_edit() ) {

		// Exclude name field.
		$exclude_fields = bp_xprofile_fullname_field_id();

		// Merge with existing if populated.
		$args['exclude_fields'] = bphnf_merge_excluded_fields( $args['exclude_fields'], $exclude_fields );

	}

	return $args;

}

add_filter( 'bp_xprofile_get_groups', 'bphnf_intercept_profile_fields_query', 100, 2 );

/**
 * Filter the xProfile query to exclude the BuddyPress "Name" field from display.
 *
 * This callback excludes the default BuddyPress "Name" field on all admin screens
 * where Profile Fields can be managed.
 *
 * @since 1.1
 *
 * @param array $groups The array of xProfile groups.
 * @param array $args The array of arguments.
 * @return array $groups The modified array of xProfile groups.
 */
function bphnf_intercept_profile_fields_query( $groups, $args ) {

	// Bail if not in admin.
	if ( ! is_admin() ) {
		return $groups;
	}

	// Exclude name field.
	$args['exclude_fields'] = bp_xprofile_fullname_field_id();

	// Re-query the groups.
	$groups = BP_XProfile_Group::get( $args );

	// --<
	return $groups;

}

/**
 * Merge possibly comma-delimited lists of excluded fields.
 *
 * @since 1.0
 *
 * @param string $excluded_fields Comma-delimited list of fields already excluded.
 * @param string $exclude_fields Comma-delimited list of fields requiring exclusion.
 * @return string $excluded_fields Comma-delimited list of all fields to be excluded.
 */
function bphnf_merge_excluded_fields( $excluded_fields, $exclude_fields ) {

	// If params are not arrays already, convert them.
	if ( ! is_array( $excluded_fields ) ) {
		if ( ! empty( $excluded_fields ) ) {
			$excluded_fields = explode( ',', $excluded_fields );
		} else {
			$excluded_fields = [];
		}
	}
	if ( ! is_array( $exclude_fields ) ) {
		if ( ! empty( $exclude_fields ) ) {
			$exclude_fields = explode( ',', $exclude_fields );
		} else {
			$exclude_fields = [];
		}
	}

	// Merge with existing.
	$excluded_fields = array_unique( array_merge( $excluded_fields, $exclude_fields ) );
	return implode( ',', $excluded_fields );

}

Thanks @christianwach.
It is working perfect now.
The updated on this gist is very welcome also.

Next time i will make screenshots to make it more easy to understand