Why is a registrants name both on the registered list and on the payment pending list?

I only realized today that I had people who registered but whose payments have not gone through.  Why would they be stuck there?  Would they be notified in any way to know that their payment did not go through?  Also, why are some people on that list, and also on the completed list?  Did they fill out two registration forms?  Thanks for your help!

I think you are referring to the Incomplete Payment. Incomplete means that someone failed to send the payment after being redirected to the Paypal payment page. Either they close the payment window or there's a problem in their payment.

https://www.jotform.com/help/564-how-to-view-incomplete-payments-of-your-payment-forms/

Would they be notified in any way to know that their payment did not go through?

If you would like to send and receive an email for incomplete payment, you will have to enable the incomplete payment email. Here's our guide for that: 

https://www.jotform.com/help/273-How-to-setup-Incomplete-Payment-Notification-E-mail

Make sure to select Notifiers and Autoresponders from the list:

Also, why are some people on that list, and also on the completed list?  Did they fill out two registration forms? 

If you see the submission in the grid list, that means the payment went through. If not, that means incomplete payment (reason above). And yes, probably your customer tried to submit again just to complete the payment. 

Thank you and let us know if you have any further questions.