ROBERT MILLER JR., vice chairman of the Chrysler Corp., has been named new chairman of the Detroit Symphony Orchestra, replacing Walter McCarthy Jr., chairman of Detroit Edison Co. Miller will take the reins Sept. 1 as music director Gunther Herbig prepares to leave his post at the end of the 1989 season to go to the Toronto Symphony.

In addition, the orchestra has a deficit of several million dollars. A musicians' strike last fall, prompted by a request that the musicians take a sharp pay cut, forced the cancellation of the season until Christmas.Miller, who engineered the financial bailout plan that saved Chrysler from bankruptcy, said he looks forward to the challenge of chairing the orchestra.

ON AGAIN, OFF AGAIN: The Dallas Ballet has failed to raise its needed $1.3 million and will not open in Dallas this fall. The company will tour Denmark Sept. 2-12 and may go to Spain also, but will not open its scheduled of "Swan Lake" on Oct. 13.