Order Post Type Navigation

optn.php

<?php
/**
 * Order Post Type Navigation
 *
 * @package optn
 * @author  Bernhard Kau
 * @license GPLv3
 *
 * @wordpress-plugin
 * Plugin Name: Order Post Type Navigation
 * Plugin URI: https://gist.github.com/2ndkauboy/64ddd0ba066208c8ea694f3cecf587ed
 * Description: Order the Post Type Navigation by name.
 * Version: 1.0.0
 * Author: Bernhard Kau
 * Author URI: https://kau-boys.de
 * Text Domain: optn
 * License: GPLv3
 * License URI: https://www.gnu.org/licenses/gpl-3.0.txt
 */

/**
 * Register a custom post type `sponsor`.
 */
function optn_register_post_type() {
	register_post_type(
		'sponsor',
		array(
			'label'       => __( 'Sponsor', 'optn' ),
			'public'      => true,
			'has_archive' => true,
			'show_ui'     => true,
		)
	);
}
add_action( 'init', 'optn_register_post_type' );

/**
 * Order sponsors by name.
 *
 * @param WP_Query $query The WP_Query instance (passed by reference).
 */
function optn_pre_get_posts_order_by_name( $query ) {
	if ( is_admin() || ! $query->is_main_query() ) {
		return;
	}

	if ( is_post_type_archive( 'sponsor' ) ) {
		$query->set( 'orderby', 'name' );
		$query->set( 'order', 'ASC' );
	}
}
add_action( 'pre_get_posts', 'optn_pre_get_posts_order_by_name' );

/**
 * Set the `WHERE` clause to order adjacent partners by name.
 *
 * @param string  $where          The `WHERE` clause in the SQL.
 * @param bool    $in_same_term   Whether post should be in a same taxonomy term.
 * @param array   $excluded_terms Array of excluded term IDs.
 * @param string  $taxonomy       Taxonomy. Used to identify the term used when `$in_same_term` is true.
 * @param WP_Post $post           WP_Post object.
 *
 * @return string
 */
function optn_get_adjacent_post_where( $where, $in_same_term, $excluded_terms, $taxonomy, $post ) {
	if ( 'sponsor' !== $post->post_type ) {
		return $where;
	}

	return preg_replace( '/p.post_date (.) ([^A-Z]+)/', "p.post_title $1 '{$post->post_title}' ", $where );
}
add_filter( 'get_previous_post_where', 'optn_get_adjacent_post_where', 10, 5 );
add_filter( 'get_next_post_where', 'optn_get_adjacent_post_where', 10, 5 );

/**
 * Set the `ORDER BY` clause to order adjacent partners by name.
 *
 * @param string  $order_by The `ORDER BY` clause in the SQL.
 * @param WP_Post $post     WP_Post object.
 * @param string  $order    Sort order. 'DESC' for previous post, 'ASC' for next.
 *
 * @return string
 */
function optn_get_adjacent_post_sort( $order_by, $post, $order ) {
	if ( 'sponsor' !== $post->post_type ) {
		return $order_by;
	}

	return preg_replace( '/p.post_date/', 'p.post_title', $order_by );
}
add_filter( 'get_previous_post_sort', 'optn_get_adjacent_post_sort', 10, 3 );
add_filter( 'get_next_post_sort', 'optn_get_adjacent_post_sort', 10, 3 );

Blog post for this snippet: https://kau-boys.com/2492/web-development/order-post-type-navigation-by-name