There is no single term satisfactory on all points for use when referring to THAT. The name "Overself" is no exception to this situation. But to those who object to this coinage of a new word, the answer is best given by the editor of the latest edition of Fowler's Modern English Usage, Sir Ernest Gowers: "I'm all in favour of new words. How else would a language live and flourish?"
-- Notebooks Category 22: Inspiration and the Overself > Chapter 3: The Overself's Presence > # 270