In order to know who has completed the form and who has not, go to 'Collect' settings page and set the 'Multiple responses' setting to 'Restrict to response code and URL'.
Distribute the unique URLs issued and write down which unique URLs did you give to which respondents. After collecting responses you can check the status of response at 'Response status' tab in 'Analyze' page.
For more information on ‘Restrict to response code and URL’, please check Moaform features > Collect > Multiple responses.