Show custom taxonomy in theme

If you want to list out the custom taxonomy you have to use get_terms function

For your requirement instead of creating new taxonomy you can modify the default category it self

function custom_change_cat_object() {
    global $wp_taxonomies;
    $labels = &$wp_taxonomies['category']->labels;
    $labels->name="Author";
    $labels->singular_name="Author";
    $labels->add_new = 'Add Author';
    $labels->add_new_item = 'Add Author';
    $labels->edit_item = 'Edit Author';
    $labels->new_item = 'Author';
    $labels->view_item = 'View Author';
    $labels->search_items="Search Authors";
    $labels->not_found = 'No Authors found';
    $labels->not_found_in_trash="No Authors found in Trash";
    $labels->all_items="All Authors";
    $labels->menu_name="Author";
    $labels->name_admin_bar="Author";
}
add_action( 'init', 'custom_change_cat_object' );