Having just done this ourselves we simply filed a new Affidavit. The only difference being in the title we were told to write "Amended Affidavit of Claiming Successor".
The new/amended affidavit was basically the same as original but will the changes and the title change. The court used this copy in place of the original that we had filed. There was no additional filing fee for this, we only paid for the certified copies that we needed.