How do I add additional options to customer gender?

Can you do this in the database? Yes. Should you? No.

Rule #1 about Fight Magento Club - Never touch the database directly.

So create an install script. There are dozens of tutorials out there for that. Once you have that set up, the process isn't dissimilar from adding options to other EAV option types:

<?php


$installer = $this;

/* @var $installer Mage_Customer_Model_Entity_Setup */
$installer->startSetup();

$tableOptions        = $installer->getTable('eav_attribute_option');
$tableOptionValues   = $installer->getTable('eav_attribute_option_value');

// add options for level of politeness
$attributeId = (int)$installer->getAttribute('customer', 'gender', 'attribute_id');


// add option
$data = array(
    'attribute_id' => 'Non-Binary, Prefer not to say',
    'sort_order'   => 99,
);
$installer->getConnection()->insert($tableOptions, $data);

// add option label
$optionId = (int)$installer->getConnection()->lastInsertId($tableOptions, 'option_id');
$data = array(
    'option_id' => $optionId,
    'store_id'  => 0,
    'value'     => $label,
);
$installer->getConnection()->insert($tableOptionValues, $data);



$installer->endSetup();