Would you tell us the version of Acrobat Reader for iOS (iPad/iPhone) that you are using? The latest version is 15.4 (as of February 6, 2016).
The Help link that was provided in reply #1 above contains the information for Reader that is older than version 15.x. It may not be the right one for your Reader app.
Please refer to the following FAQ document if you have the latest version of Acrobat Reader for iOS.
The important thing to note is that the options to perform file operations (such as Rename, Duplicate, Delete) are not available in the Recent section. Please make sure to switch the file location to Local for locally stored files on your iPad/iPhone, Document Cloud for cloud files, etc. first.
Hope this helps.