Read the help of the app.
[topic moved to Reader/Acrobat DC for Mobile forum]
Open Acrobat reader on your iPad.
Go to location like Local, Document Cloud, etc at the center top.
Select the Check mark key at the top right and then select the file which you would like to rename.
Once the file is selected click on the icon at the bottom right (2nd from right) to rename the file.
This will bring a Popup to give it a new name.
Thanks for your help!!