Print the associated categories of the current post starting with parent (with option to remove href)

Here is code snippet from WordPress that display the categories (or terms from other taxonomies) assigned to a post ordered by parent-child category relationship.This example must be used inside the loop.

$taxonomy = 'category';

// Get the term IDs assigned to post.
$post_terms = wp_get_object_terms( $post->ID, $taxonomy, array( 'fields' => 'ids' ) );

// Separator between links.
$separator=", ";

if ( ! empty( $post_terms ) && ! is_wp_error( $post_terms ) ) {

    $term_ids = implode( ',' , $post_terms );

    $terms = wp_list_categories( array(
        'title_li' => '',
        'style'    => 'none',
        'echo'     => false,
        'taxonomy' => $taxonomy,
        'include'  => $term_ids
    ) );

    $terms = rtrim( trim( str_replace( '<br />',  $separator, $terms ) ), $separator );

    // Display post categories.
    echo  $terms;
}

Information on this page may help you to adjust the code to your requirements.
I hope this will help.