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 {{product_name}} , then get the block in product page:
$html = Mage::app()->getLayout()->createBlock('cms/block')->setBlockId('block_id')->toHtml();
and then inject your product name:
echo str_replace("{{product_id}}",$product->getId(),$html);