Show only 1 term of a current posts taxonomy

This is more PHP than WordPress, but wp_get_post_terms returns a numerically indexed array, so all you need is basic PHP array syntax to grab the first item.

$terms = wp_get_post_terms($post->ID, 'custom_cat');

print_r($terms[0]->name);

You don’t specify which item you want. This will get you last item:

$terms = array_pop($terms);
print_r($terms);