I’ll start by saying that I have no background in php.
I need to embed a shortcode to display the name of the specific taxonomy the post is associated with.

I found an answer that seems close to what I’m looking for.
The answer from this page:
Displaying taxonomy term instead of category in title

The code shown there in the solution is:

// Get taxonomy terms specifc to current post
$terms =  get_the_terms( $post->ID , 'your-taxonomy-name-here' );

foreach ( $terms as $term ) {
    echo ' <a href="' .esc_url( home_url( '/' ) ). $term->slug . '" title="' . $term->name . '" ' . '>' . $term->name .'</a>    ';
}

According to this code I tried the following code, without success:

// Get taxonomy terms specifc to current post
$terms =  get_the_terms( $post->ID , 'dish_type' );

foreach ( $terms as $term ) {
    echo ' <a href="' .esc_url( home_url( '/' ) ). $term->slug . '" title="' . $term->name . '" ' . '>' . $term->name .'</a>    ';
}
  add_shortcode('dish_type', 'get_the_terms');

Remarks:

1. I don’t need a link to the taxonomy.
2. I tried to replace ‘your-taxonomy-name-here’ with the Taxonomy Key: dish_type
3. Did I correctly add the add_shortcode?

I would appreciate your help