Is there a way I can return terms by name using a shortcode?

This is the solution to get post terms by taxonomy by shortcode:

/**
 * Custom shortcode to get terms
 */

function ALC_post_terms_by_taxonomy( $atts ) {

    global $post;

    $taxonomyTerms = wp_get_post_terms( $post->ID, $atts['taxonomy'], 'orderby=name&hide_empty=0' );

    $term_array = array();
    foreach ($taxonomyTerms as $taxonomyTerm) {
        $term_array[] = $taxonomyTerm->name;
    }

    return implode( ', ', $term_array );
}
add_shortcode('get_terms_by_taxonomy', 'ALC_post_terms_by_taxonomy');

And you can use it by this shortcode:

[get_terms_by_taxonomy taxonomy="taxonomyname"]