Should the editor's name be included in a rebuttal letter?
One thing to do is to write two documents:


a short letter to the Editor, summarizing your rebuttal in a few sentences;
a detailed Answer to Reviewers, including line-by-line response to all comments and suggestions of the Referees.


Note that the Editor not necessarily has enough time to read through all the detailed response him/her-self, but the presence of this document re-assures that the discussion between Authors and Referees is going in the right direction. If you experience problems addressing Referees' questions, or disagree with them significantly, you should mention this in the letter to the Editor.