How to use hook_form_alter to target a specific drupal commerce form?
To add or alter the pane forms on the checkout page, for maximum compatibility, you should use the Commerce API.

Define new panes in:

hook_commerce_checkout_pane_info

Alter existing panes: 

hook_commerce_checkout_pane_info_alter

For example, you could alter the checkout_form callback for a checkout pane to add your customizations.


  checkout_form($form, &amp;$form_state, $checkout_pane, $order): returns form elements for the pane’s checkout form fieldset


You could also add your own custom checkout pane for your custom design there.

You can refer to the existing pane callback to first include or replicate the checkout pane. 

Note: I posted a similar answer for adding a custom validate handler to a checkout pane a while ago here: https://drupal.stackexchange.com/a/87061/7153