Override the display name for a user in the PMPro Member Directory and Profile pages by changing the display name to user meta, e.g. company name.

pmpro-member-directory-change-display-name.php

<?php
/**
 * This recipe changes a user's display name on directory and
 * profile pages with custom meta data if the data is available.
 *
 * This requires the Member Directory and Profile Pages Add On version 1.0 or later.
 * https://www.paidmembershipspro.com/add-ons/member-directory/
 *
 * A use case for this would be to display a company name instead of the user's name(s).
 *
 * 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 my_pmpro_member_directory_custom_display_name( $display_name, $user ) {

	#--- SETTINGS ---#
	$meta_key = 'company_name'; // change this to the meta key you want to use
	/* That's it, no further editing required */

	// Get user meta
	$custom_name = get_user_meta( $user->ID, $meta_key, true );

	// If we have a custom name, use it
	if ( $custom_name ) {
		// Let's override the display name with the custom name.
		$display_name = $custom_name;
	}
	return $display_name;
}
add_filter( 'pmpro_member_directory_display_name', 'my_pmpro_member_directory_custom_display_name', 10, 2 );