This worked for me on my iPad. Assuming your have Adobe Reader open and can see your document on the screen.
1- Click (tap) on the tick box, top RHS corner of screen. This is a selector tool.
2- Click (tap) in your doc. This will select it and put a tick next to it on the LHS.
3. Down the bottom there now appears a toolbar. Tap on the icon on that toolbar that looks like a square box with an I and two dots inside it. This is the rename tool.
4. Rename your doc by typing in the dialog box that will now appear.