It depends how you're fetching the category. But if you've defined the template when setting up the categories it would be called be within a var called 'category', which would be a category object. You should then be able to access it using:
{{ category.title }}
If, on the other hand, you were getting the category via a slug in the URL, you would do something like:
{% set category = craft.categories.group('productType').slug(craft.request.lastSegment).first %}
{{ category.title }}
UPDATE: Following on from your updated question, you've already got the category as an object so there is no need to get it again. Try replacing:
// THIS IS YOUR LOOP, BTW
{% for category in craft.categories.group('productType').find() %}
<header class="flush"><h1>{{ category.title }}</h1></header>
{% endfor %}
with:
{{ category.title }}
But you might need to add a conditional in case the page is loaded without a category. Something like:
{% if category | length %}
{{ category.title }}
{% endif %}