Show Child category for given entry

Hello,

Is there a way to ONLY show a child category for an entry within an entries loop?

Lets say I have categories such as:

• Blog

  • design
  • work
  • something else

• Social

  • lastfm
  • flickr

I then submit a post to the child cat, design.

Then my entries loop:

{exp:channel:entries channel="tumblelog"}
{categories}

 {category_name} <!-- outputs : blog design -->

{/categories}
{/exp:channel:entries}

This outputs, blog, design… BUT I only want to ever show the single, child category for a given entry… NEVER showing the parent category.

Is this possible?

Please note it vital I keep “Auto-Assign Category Parents” on as I do need this relationship elsewhere.