Does this work?
global $post; // make sure the post object is available
$slug = $post->post_name; // get the slug
// insert the slug into your query
$args = array(
'post_type' => 'client_prop',
'posts_per_page' => 10,
'tax_query' => array(
array(
'taxonomy' => 'prop_neighborhood',
'field' => 'slug',
'terms' => $slug,
)
)
);