It can be a little tricky at first until you get the hang of where everything is. Here is the process, the steps are illustrated below with screen captures.
1. Tap the Home icon, and make sure you select My Documents."
2. In My Documents, you must have "Local" or "Document Cloud" selected.
3. Click the check icon in the upper right to enter selection mode.
4. Tap the hollow circle next to a document to select it.
5. With a document selected, you can see the action bar at the bottom. Choose the rename icon.
6. Rename the document in the pop up box and tap "Rename."
screen shots here:
Thank you, Mike. Never would have figured that out, having to "Select" the file before the bottom menu bar appears!