<?php
$term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) );
echo $term->name; // will show the name
echo $term->slug;
?>
<?php
$terms = get_the_terms( $post->ID, 'event_category' );
foreach($terms as $term) {}
?>
<span class="label label-blue"><?php echo $term->name; ?></span>