Deleting and moving files must be done through your cloud storage provider. You can't do this through the Document picker.  So you will need to open your cloud file store - whether that's Dropbox, Google drive, One drive etc and do your moving, deleting and renaming from there.   

Another way you might rename a file is when you make a copy - you can simply click on Documents > Make a copy > Same Tab/New tab and save the file in a new location with a new filename.

If you delete a file it will still appear in the Recent Files panel of the Document picker but you will not be able to open it - you'll receive a warning that the file couldn't be found in the cloud drive. 

If you tap Re-try or Cancel the picker will refresh and the deleted doc will no longer be visible. 

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