How do I allow people to submit multiple forms with the same name?

I am not sure if I understood your concern correctly.

JotForm's online forms can be submitted by your users multiple times, unless you enable the form limitation. They can submit the same information as long as they open the form and click the submit button.

Could you please elaborate? What is the exact problem you are getting?

Here are some guides on how to limit the submission of a form:

https://www.jotform.com/help/137-How-to-limit-submissions-in-a-form 

https://www.jotform.com/help/223-How-to-set-Form-Limits-Based-on-a-Unique-Question 

I hope that helps.