Indeed, it's the correct file you're searching for. And the correct spot.
You have the code:
<span id="hikashop_product_name_main" class="hikashop_product_name_main">
<?php
if (hikashop_getCID('product_id')!=$this->element->product_id && isset ($this->element->main->product_name))
echo $this->element->main->product_name;
else
echo $this->element->product_name;
?>
</span>
That you should replace with just:
<?php echo $this->element->main_product_name; ?>
Then, you can add that where you want the variant text:
<span id="hikashop_product_name_main" class="hikashop_product_name_main"></span>
And in the "show" view file, you can change
<?php echo $variant->product_name;?>
by:
<?php echo $variant->characteristics_text;?>