<?php $current_term = get_queried_object()->term_id; ?>
<?php $term_obj_list = get_the_terms( $post->ID, 'taxonomy_name' ); ?>
$term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) ); echo $term->name; // will show the name echo $term->slug; // will show the slug