Getting a subcategory by a category name in Magento

I have a category called "designers" that has N subcategories; the des开发者_JS百科igner names. For a given product, I want to extract all the designer names. So

    For current product instance, show active/selected subcategories by category 'designer'

How is this accomplished in Magento? I've search and tried at least 5x different google results and none seem to get me the correct answer.

TIA.

Edit:

Category

• Designers

  Sub-Category

  • D1

  • D2

Product

• P1 contains (Designers->D1)

So, for P1, I'd like to get the value D1.