How to display singular_name of custom taxonomy?

As far as I’m aware, your question has been answered here.

You’re getting the singular_name correctly, all you need to do is echo it.

<?php $taxonomies = get_object_taxonomies( $post );
foreach ( $taxonomies as $taxonomy ) {

$term_name = $taxonomy->labels->singular_name;

echo $term_name;

the_terms( $post->ID, $taxonomy, '<span class="e-article__category__item"><strong>' . $term_name . ': </strong>  ', ", ", '</span>' );
} ?>