First get the data
$data = get_user_meta( $user_id, 'service_name', true);
You find an array of all entries in $data. You can do it this way:
<input type="checkbox" name="service_name[]" value="Architecture" <?php echo in_array('Architecture', $data) ? 'checked' : ''); ?>>Architecture<br>
Untested, but should work.