File Upload with Required Label

Do you know if there is any way (or widget) to have a file upload that the user can upload multiple files, but they have to label the files that they upload?

You can set the File Upload field to allow multiple file uploads.

Here's how: 

You can also use the information on this blog post, Jotform-Now-Supports-Multiple-File-Uploads, as your reference. 

Here's a widget that you can also use. 

Drag and Drop Upload widget

With regards to labelling the uploaded files, to my understanding, you want to know if there is a way to label or set a file name for the uploaded files, is that correct? What I can suggest is you can just ask your submitters to set a proper file name for their files before they upload it. This way, the file name will just appear on the list of uploaded files of the File Upload or Drag and Drop Upload widget.

You can still delete uploaded files in the File Upload fields after it is being uploaded, however, in the Drag and Drop widget, once the file is uploaded completely(after clicking the "Begin Upload" button), you will not be able to delete it anymore.

I hope this helps. If this is not what you are referring to, please feel free to get back to us with more details so we can further assist you.

Thank you.