Can I save my completed forms to different client files?

If you are looking to add the forms into folders, please follow this guide: https://www.jotform.com/help/204-How-to-Add-or-Group-Your-Forms-into-Folders

If that is not what you mean, could you please explain further what you need?

I send each client 4 to 5 forms to complete before their appointment. When they send them back, I get the submission. How do I organize each client’s submissions to a different file? So say John Smith filled out his forms and returned them to me. I want John Smith to have a file so I can go back and look at his files and charts/answers at any future appointments. I need to be able to access this information by client name.
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The current submissions page does not allow to apply filters, so all data is stored in the submissions page. However, we are developing the new version of the submissions page. It has not been fully released yet, but you can access this way:

1) Go to the submissions page of your form: https://www.jotform.com/help/269-How-to-View-Form-Submissions

2) Then, replace the word "submissions" for "sheets" in the URL and load it.

There you will be able to create a new tab to view the submissions and apply filters.  Example:

Let us know if you need more help.