Get custom taxonomy name from custom post

Blueprint

1. Get all taxonomies.
2. Loop through them.
3. Get terms for current post.

Code

// Suppose you already have $post
foreach ( get_object_taxonomies( $post ) as $taxonomy ) {
    foreach ( get_the_terms( $post->ID, $taxonomy ) as $term ) {
        // Do whatever you'd like with $term
        echo $term->name;
    }
}

References

• get_object_taxonomies
• get_the_terms