In the current form of our extensions system, that would be very difficult.
You would have to change the name of the extension in all possible places in the files where the name is mentioned, both in the code and in the tables it would add to the database. If you would miss one instance of a name, that might already mess the entire extension up.
I think your best shot would be to ask in the Recent Topics extension support area and explain what you want to do.
It might be possible to edit the existing extension to suit your needs instead of trying to duplicate it into two separate extensions.