What a mess. Adobe decided to push the new "DC" on my tablet. Now there is no document tab, all my PDF files are gone or in-accessible, and I can find no option to rename new downloaded PDF files. Complete revamp really was a good idea, right? Just when I getting used to working around the KitKat 4.4 SD card issue, now this. I'm going back to paper and pencils!!! This is so incredibly PRODUCTIVE, learning a whole new buggy interface after so many years of getting comfortable with "Reader".... I don't need or want the cloud, I just want to work with my documents on my tablet - THEN, let me decide what I want to do with them. Sorry, I am just so frustrated with having to completely RE-LEARN how to do something so basic every time some software gets "improved", or "updated".
Could you try if this video helps: https://www.youtube.com/watch?v=fTrTPR9LEq8.
Also, for renaming the document, you would need to use a third party file manager such as AndExplorer or ES File Manager.