If you have a paid subscription of Adobe Acrobat Pro DC, sign in with your AdobeID in the Acrobat Reader Mobile app.
All editing features are unlocked once you sign in with the AdobeID that is associated with your paid subscription of Acrobat Pro DC.
Otherwise , you'll be limited to reading, viewing, fill and sign, and print PDF dcouments.
The feature you're inquiring about is named "Save as Copy".
If you already do have a paid active subscription, thenn make sure your app is fully updated to its latest version.
If I am not incorrect, that is a new feature that came out during recent updates.
NOTE: When you employ this feature, the filename will be renamed automatically; "Save as Copy" will append a suffix in number format inside a parenthesis at the end of the original file name, for example: myPDFtest.pdf(1)
You can also manually change a file name in your mobile device by navigating to the folder (or directory) where you've downloaded the source document, or after saving a copy of that source file to another location (either saved locally or cached online via Cloud space services).