Show a list of the sponsored member names on the parent's profile page on the Member Directory's Profile Page

show_sponsored_child_name_pmpro_member_profile_after.php

<?php
/**
 * Show a list of the sponsored (child) member accounts on the parent's profile page on the Member Directory's Profile page.
 *
 * Display sponsored member's full names of user has both first and last name meta, otherwise default to their display name.
 *
 * You can add this recipe to your site by creating a custom plugin
 * or using the Code Snippets plugin available for free in the WordPress repository.
 * Read this companion article for step-by-step directions on either method.
 * https://www.paidmembershipspro.com/create-a-plugin-for-pmpro-customizations/
 */
function show_sponsored_child_accounts_pmpro_member_profile_after( $pu ) {
	// Let's only do this if PMPro Sponsored Members is active.
	if ( ! function_exists( 'pmprosm_getChildren' ) ) {
		return;
	}

	// Get sponsored member's user IDs
	$sponsored_ids = pmprosm_getChildren( $pu->ID );

	if ( empty( $sponsored_ids ) ) {
		return;
	}

	$sponsored_list = new WP_User_Query(
		array(
			'include' => $sponsored_ids,
			'orderby' => 'name',
			'order'   => 'ASC',
		),
	);

	$sponsored_members = $sponsored_list->get_results();
	if ( ! empty( $sponsored_members ) ) {
		echo '<strong>Sponsored Members</strong>';
		echo '<ul>';
		foreach ( $sponsored_members as $sponsored_member ) {
			$member_id  = $sponsored_member->ID;
			$first_name = get_user_meta( $member_id, 'first_name', true );
			$last_name  = get_user_meta( $member_id, 'last_name', true );
			$name       = $first_name && $last_name ? $first_name . ' ' . $last_name : $sponsored_member->data->display_name;

			echo '<li>' . esc_html( $name ) . '</li>';
		}
		echo '</ul>';
	}
}
add_action( 'pmpro_member_profile_after', 'show_sponsored_child_accounts_pmpro_member_profile_after' );

To list sponsored member account users' display names instead of first and last names see https://gist.github.com/kimcoleman/38d4a32604002c5d88938a0d3f36233e