Show Subcategory Name Instead of Parent Category

$terms = get_terms( ['taxonomy' => 'some-taxonomy', 'parent' => 123 ] );
// or
$categories = get_categories( [ 'parent' => 123 ] );

Where the parent id is the one you want to get the subcategory from. This gives you all subcategories/-terms in an array. You can access data like name or term_id. For getting the link you can use get_category_link or get_term_link.