How do I add another field for the third name in the Full name field?

In the Full Name field, you can only enable the suffix, pre-fix and middle name. You can find this in the "Options" tab of the Name properties, here's a screenshot:

We do have a widget called Multiple Text Fields widget. This widget will generate the field labels and the input boxes for each of the listed fields. Here's a demo form.

Here's a guide on How-to-Add-a-Widget-to-Your-Form.

Hope that helps. Thank you.