How to reverse first name and last name globally

in magento full name are comming from addNameToSelect() function of class Mage_Customer_Model_Resource_Customer_Collection and getName() function of class Mage_Customer_Model_Customer.You need change there by rewrite classes.

  <global>
    <models>
      <magento70422>
        <class>Stackexchange_Magento70422_Model</class>
      </magento70422>
            <customer_resource>
                <rewrite>
                    <customer_collection>Stackexchange_Magento70422_Model_Customer_Resource_Customer_Collection</customer_collection>
                </rewrite>
            </customer_resource>
            <customer>
                <rewrite>
                    <customer>Stackexchange_Magento70422_Model_Customer_Customer</customer>
                </rewrite>
            </customer>
    </models>
  </global>

Rewrite class of Mage_Customer_Model_Customer

<?php
class Stackexchange_Magento70422_Model_Customer_Customer extends Mage_Customer_Model_Customer
{

   public function getName()
    {
        $name = '';
        $config = Mage::getSingleton('eav/config');
        if ($config->getAttribute('customer', 'prefix')->getIsVisible() && $this->getPrefix()) {
            $name .= $this->getPrefix() . ' ';
        }
        //$name .= $this->getFirstname();
    $name .=  $this->getLastname();
        if ($config->getAttribute('customer', 'middlename')->getIsVisible() && $this->getMiddlename()) {
            $name .= ' ' . $this->getMiddlename();
        }
        //$name .=  ' ' . $this->getLastname();
    $name .= ' ' . $this->getFirstname();   
        if ($config->getAttribute('customer', 'suffix')->getIsVisible() && $this->getSuffix()) {
            $name .= ' ' . $this->getSuffix();
        }
        return $name;
    }
}

Rewrite resource collection class of Mage_Customer_Model_Resource_Customer_Collection is below:

<?php
class Stackexchange_Magento70422_Model_Customer_Resource_Customer_Collection extends Mage_Customer_Model_Resource_Customer_Collection
{
public function addNameToSelect()
    {
        $fields = array();
        $customerAccount = Mage::getConfig()->getFieldset('customer_account');
        foreach ($customerAccount as $code => $node) {
            if ($node->is('name')) {
                $fields[$code] = $code;
            }
        }

        $adapter = $this->getConnection();
        $concatenate = array();
        if (isset($fields['prefix'])) {
            $concatenate[] = $adapter->getCheckSql(
                '{{prefix}} IS NOT NULL AND {{prefix}} != \'\'',
                $adapter->getConcatSql(array('LTRIM(RTRIM({{prefix}}))', '\' \'')),
                '\'\'');
        }
       // $concatenate[] = 'LTRIM(RTRIM({{firstname}}))';
        $concatenate[] = 'LTRIM(RTRIM({{lastname}}))';

        $concatenate[] = '\' \'';
        if (isset($fields['middlename'])) {
            $concatenate[] = $adapter->getCheckSql(
                '{{middlename}} IS NOT NULL AND {{middlename}} != \'\'',
                $adapter->getConcatSql(array('LTRIM(RTRIM({{middlename}}))', '\' \'')),
                '\'\'');
        }
       // $concatenate[] = 'LTRIM(RTRIM({{lastname}}))';
    $concatenate[] = 'LTRIM(RTRIM({{firstname}}))'
        if (isset($fields['suffix'])) {
            $concatenate[] = $adapter
                    ->getCheckSql('{{suffix}} IS NOT NULL AND {{suffix}} != \'\'',
                $adapter->getConcatSql(array('\' \'', 'LTRIM(RTRIM({{suffix}}))')),
                '\'\'');
        }

        $nameExpr = $adapter->getConcatSql($concatenate);

        $this->addExpressionAttributeToSelect('name', $nameExpr, $fields);

        return $this;
    }
}

In \app\code\core\Mage\Customer\Model\Customer.php there is a method called getName() that looks like this:

public function getName()
    {
        $name = '';
        $config = Mage::getSingleton('eav/config');
        if ($config->getAttribute('customer', 'prefix')->getIsVisible() && $this->getPrefix()) {
            $name .= $this->getPrefix() . ' ';
        }
        $name .= $this->getFirstname();
        if ($config->getAttribute('customer', 'middlename')->getIsVisible() && $this->getMiddlename()) {
            $name .= ' ' . $this->getMiddlename();
        }
        $name .=  ' ' . $this->getLastname();
        if ($config->getAttribute('customer', 'suffix')->getIsVisible() && $this->getSuffix()) {
            $name .= ' ' . $this->getSuffix();
        }
        return $name;
    }

Change it by simply inversing getFirstname with getLastname. To change this without modifying the core file, you can copy this file to the local code pool, or create your own module and rewrite this method in it.