As per Magento Standard.
In Manage Customer Grid you can see the Full name with Prifix FirstName LastName
.
You have to override the Customer Grid and Add new Field In grid.
Step 1: app\code\core\Mage\Adminhtml\Block\Customer\Grid.php
Copy this file to app\code\local\Mage\Adminhtml\Block\Customer\Grid.php
.
Step 2: Find _prepareColumns()
method in this file.
Step 3: added below code.
$this->addColumn('firstname', array(
'header' => Mage::helper('customer')->__('First Name'),
'index' => 'firstname'
));
$this->addColumn('lastname', array(
'header' => Mage::helper('customer')->__('Last Name'),
'index' => 'lastname'
));
Step 4 : and comment below lines.
$this->addColumn('name', array(
'header' => Mage::helper('customer')->__('Name'),
'index' => 'name'
));
Step 5: You can search with now Name and LastName also.
There is another way is also you can override the Mage_Adminhtml_Block_Customer_Grid
and added this filed also.
Thanks let me if any question.