how can I copy a registration form and rename so that I keep the original form as well?

In a text file it would just be a "save as" then I'd have two.

It is possible to clone forms from your own account to create a new copy:

https://www.jotform.com/help/27-How-to-clone-an-existing-form-from-your-account

It is also possible to clone forms from other users:

https://www.jotform.com/help/42-How-to-Clone-an-Existing-Form-from-a-URL

Both of which will create a new copy of the form in your account without having any impact on the original.