How to identify who moved a Folder in SharePoint

Chris_Clark1968 Are you moving folders from one document library to same/another document library "within" same/another SharePoint site?

If yes, you can refer to Modified By column to get the name of user who moved (modified the folder last time) the folder in SharePoint. You can add the column in document library view like: 

Note: If another user have changed any folder properties after moving it - Modified by column will show the another user's name and not the name of user who moved it. In that case, you may be able to get some information from version history.

You can go to the version history page of folder using URL like: 

https://contoso.sharepoint.com/sites/MySite/_layouts/15/Versions.aspx?list={6fa99ffb-95ab-4196-aeb5-a9e3e0a7af66}&ID=1

Where 1 is an item ID of folder: 

And 6fa99ffb-95ab-4196-aeb5-a9e3e0a7af66 is the GUID of your document library. You can get the GUID from Library settings page: 

Version history page will look like this: 

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