His family and company wanted to make sure that Walt's name remained a legacy, which may be why they stayed in the shadows and worked very hard to keep Walt's vision alive.
This is just rough history, but gives you a little bit about how his family carried on his name -
Walt's older brother, Roy O. Disney, remained the president of the Walt Disney Company until 1968 (died in 1971). Roy's son and Walt's nephew, Roy E. Disney, was elected to the board of directors of the Walt Disney Company in 1967, but resigned in 1977. He passed away in December, 2009.
Walt's son-in-law, Ronald W. Miller (husband of Walt's oldest daughter, Diane), became president of Walt Disney Productions in 1980 and CEO in 1983.
It was actually Roy E. Disney who fought to replace Miller with Eisner in 1984. Roy E. also fought to replace Eisner with Iger in 2005.
Walt's wife, Lillian, remarried in 1969 to John L Truyens (only 3 years!?!). He passed away in 1981. She donated $50 million to the construction of the Walt Disney Concert Hall in Los Angeles, California, which opened in 2003. Lillian died of a stroke in 1997 (which occured exactly 31 years after the death of Walt).
Walt's youngest daughter, Sharon, died of breast cancer in 1993.
He is survived by his oldest daughter, Diane, and her husband, Ronald. They have operated Silverado Vineyards Winery in Napa since 1981.
There is an interesting interview in People Magazine of Diane -
http://www.people.com/people/archive/article/0,,20127119,00.html
In 2007, Diane voiced her opinion about Neal Gabler's Walt Disney Biography
Walt Disney: The Triumph of the American Imagination - "a monstrous piece of libelous junk. My parents were not the people he creates in this book, and I cannot understand why all of you who aided and abetted Gabler in writing this book, and who praise it and promote it, can do so without suffering serious qualms."
Diane and Ronald had seven children - Chris Miller, Joanna Miller, Tamara Scheer, Jennifer Miller-Goff, Walter Elias Disney Miller, Ronald Miller and Patrick Miller.
Sharon had three - Victoria Brown, Brad Lund and Michelle Lund
I wonder where they are today?