On Constant Contact we are able to show who has registered for an event, is that feature available on JotForm ?

I am not sure what exactly you are referring to in ConstantContact. However, it is possible to integrate ConstantContact with JotForm by following the guide below: 

https://www.jotform.com/help/386-How-to-Integrate-Form-with-Constant-Contact

Please check and let us know if that helps. Let us know if you are referring something different. We will be happy to help. 

Thank you, that is not what I am asking to do.  In Constant contact, when people register for an event their name shows up on a list on our website, as more people register their name also shows up.  I am asking if that is something JotForms can replicate?

Could you share the web page URL where it displays the name so that we can take a look? If you want to display the submissions data on your webpage, you may consider generating a Grid listing report or HTML table listing report and embed it on your webpage.

Please give it a try and let us know if you need any further assistance. We will be happy to assist.