WC Vendors - Vendor Shop Name as Full Name

gistfile1.php

/**
* Format WordPress User's "Display Name" to Full Name on Login
* ------------------------------------------------------------------------------
*/

add_action( 'wp_login', 'wpse_9326315_format_user_display_name_on_login' );

function wpse_9326315_format_user_display_name_on_login( $username ) {
    $user = get_user_by( 'login', $username );

    $first_name = get_user_meta( $user->ID, 'first_name', true );
    $last_name = get_user_meta( $user->ID, 'last_name', true );
    $shop_name =  get_user_meta( $user->ID, 'pv_shop_name', true );

    $full_name = trim( $first_name . ' ' . $last_name );
	
    if ( ! empty( $full_name ) && ( $user->data->display_name != $full_name ) ) {
        $userdata = array(
            'ID' => $user->ID,
            'display_name' => $full_name,
        );	
        
        // Update Shop Name 
	if ( !empty( $full_name ) && ( $shop_name != $full_name ) ) {	 
		update_user_meta($user->id, 'pv_shop_name', $fullname); 
	}
		 
	wp_update_user( $userdata );
    }
}