Is there a built in way to collect a visitor's name and email?

Yes, please click on the link below to learn how this is done.talkjs.com/docs/Customizations/HTML_Panels.html

Side note

We’ve noticed that there’s a practical limitation currently that reduces the effectiveness of HTML panels: If you use the Popup and have it in keepOpen mode (so the popup follows the user across sites), then the HTML Panel settings get lost. That's not supposed to happen of course. A workaround is to set keepOpen to false and manually trigger the Popup to open whenever you need it, but we're also working to fix this on short notice.