How do I show the parent term on a custom taxonomy template (not the ID)?

by

Again use the get_term_by() function: 

$curr_taxonomy = get_query_var('taxonomy');
$term = get_term_by( 'slug', get_query_var('term'), $curr_taxonomy );

if ( $term !== FALSE && $term->parent > 0 )
    $parent_term = get_term_by('id', (int) $term->parent, $curr_taxonomy );
else
    $parent_term = false;