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>' );
} ?>