Get and display category name by category description

by

I’m not aware of a built-in function like “get_cat_name_by_desc()”, but you can use the description__like parameter along with get_categories() or get_terms():

$cats = get_categories( [
  'description__like' => 'foo desc',
  'hide_empty'        => false, // disabled for testing purposes
] );
echo isset( $cats[0] ) ? $cats[0]->name : 'No categories found.';