I was working on a project and need to show only the name of first category assigned to a post. The below code helped me achieve that quickly.
$categories = get_the_category();
if ( ! empty( $categories ) ) {
echo '<a href="' . esc_url( get_category_link( $categories[0]->term_id ) ) . '">' . esc_html( $categories[0]->name ) . '</a>';
}