As far as adding a name field and making both required, that's on Constant Contact's side. I assume there is a setting when building a form to make items required (I'm not a CC user, so unsure myself).
The plugin allows the mail service to enforce their own requirements.
As far as the settings, I would assume the form action would need to be: http://visitor.constantcontact.com/d.jsp
with a email setting of: ea
with whatever hidden fields are found in the html code as provided via the instructions in the thread you linked to.
There should be a way in Constant Contact to add the name field, which you would need whatever the "name" value is in the <input type="text" name="NAME FIELD NAME"> (may look slightly different) tag.
If you shoot me a link to a page with the plugin installed, I can help ensure the settings are plugged in right.