Custom post type adding additional markup

If I understand your question, the issue is that anything within the while loop will get repeated for each post. If you want to wrap all posts in a single set of <ol></ol> tags, those must go outside that while statement.

if ( $the_query->have_posts() ) :

    // open the <ol> outside the loop
    echo '<ol class="col-neigh-title neighborhood">';

    // anything inside here is repeated for each post
    while ( $the_query->have_posts() ) :
        $the_query->the_post();
        ?>

        <li><a href="https://wordpress.stackexchange.com/questions/114741/<?php the_field("url_neighborhood' ); ?>"><?php the_field( 'neighborhood_name' ); ?></a></li>

        <?php
    endwhile;

    // close the <ol> outside the loop
    echo '</ol>';

endif;