I found the grid was being generated in the following location:
/app/code/core/Mage/Adminhtml/Block/Report/Shopcart/Abandoned/Grid.php
From there I was able to find the model being used for the abandoned shopping carts was:
$collection = Mage::getResourceModel('reports/quote_collection');
$collection->prepareForAbandonedReport(array(1));
$collection->load();
I was able to get my end goal done by adding two column to the Grid.php file. I did that by doing the following:
$this->addColumn('customer_firstname', array(
'header' =>Mage::helper('reports')->__('Customer First Name'),
'index' =>'customer_firstname',
'sortable' =>false
));
$this->addColumn('customer_lastname', array(
'header' =>Mage::helper('reports')->__('Customer Last Name'),
'index' =>'customer_lastname',
'sortable' =>false
));