How to allow Category Title to use tags?

I am not sure if you can force the system to accept markup in the category titles, and I am not sure you should even try so I am going to suggest that you hack together a kind of markdown. Use some character like * as a placeholder then…

add_filter(
  'the_category',
  function($categories) {
    $pattern = '|(\*)([^\*]+)(\*)|';
    return preg_replace($pattern,'<b>$2</b>',$categories);
  }
);

I am not sure how robust that is. I am sure the callback could be much better but it works when I test it.

Also, a lot depends on how you are displaying the categories. I am not even sure if that is the filter you need. Your questions does not provide that information.