$wpdb->prepare with LIKE returning blank array instead of rows

Your SQL doesn’t look right. It should be more like

$prep = $wpdb->prepare( "SELECT * FROM {$table_name} WHERE name LIKE '%s'", $city );

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)