How to hide category name

First of all, I wouldn’t recommend to use categories to show posts anywhere. Such approach has many consequences (it creates category archive, feeds, and so on).

But if you already have such solution, then you can use get_the_categories filter and remove given category from the list.

add_filter( 'get_the_categories', function ( $categories, $id ) {
    foreach ( $categories as $i => $term ) {
        if ( <ID_OF_CATEGORY_TO_IGNORE> == $term->term_id ) {
            unset( $categories[$i] );
        }
    }
    return $categories;
}, 10, 2 );