While there are some dynamic variables that you can use in the CMS, it's not possible to get user information without custom code.

If you embed your form in a phtml template instead of a CMS page, you can include this template in the CMS:

{{block type="core/template" template="your/form.phtml"}}

In the template, you can use any PHP code like

$customer = Mage::getSingleton('customer/session')->getCustomer();
$firstname = $customer->getFirstname();

It would be best practice to move this code to a block class. Note that you can specify the block type as well, so instead of core/template you can use any other block.

But either way, you have to add the block type to the block whitelist in "System > Permissions > Blocks" to be able to use it in the CMS (see: http://magento.stackexchange.com/a/87897/243)

While there are some dynamic variables that you can use in the CMS, it's not possible to get user information without custom code.

If you embed your form in a phtml template instead of a CMS page, you can include this template in the CMS:

{{block type="core/template" template="your/form.phtml"}}

In the template, you can use any PHP code like

$customer = Mage::getSingleton('customer/session')->getCustomer();
$firstname = $customer->getFirstname();

It would be best practice to move this code to a block class. Note that you can specify the block type as well, so instead of core/template you can use any other block.

But either way, you have to add the block type to the block whitelist in "System > Permissions > Blocks" to be able to use it in the CMS (see: https://magento.stackexchange.com/a/87897/243)