I can't find a way to directly inject a variable to the CMS,
but you could for instance insert a custom variable to the block like <code>{{product_name}}</code> , then get the block in product page:

    $html = Mage::app()->getLayout()->createBlock('cms/block')->setBlockId('block_id')->toHtml();

and then inject your product name:

    echo str_replace("{{product_name}}",$product->getName(),$html);