Descendents of Australian cricketer Sir Donald Bradman have aired their grievances about the foundation that bears his name.

They believe the cricketing legend would not support the recent expansion of the Bradman Museum into the International Cricket Hall of Fame.

"As time went by, my family and I became increasingly concerned about the way my grandpa's name was being used," Sir Donald's granddaughter, Greta Bradman, told Australian Story.

The Bradman Foundation owns a range of trademarks, including variations on Sir Donald's name, his signature and the figures 99.94 which was his batting average when he retired.

The trademarks were transferred to the Bradman Foundation when it was incorporated in 1994 as the trustee for the Bradman Museum, with money from licensing towards maintaining the museum.

"My father originally considered trademarking his name in 1991 in order to prevent and control its use," Sir Donald's son John Bradman said.

"He was upset when he found it used on a beer bottle."

Tom Bradman says his grandfather "very much controlled how those trademarks were used" when he was alive.

"He clearly expressed a written wish that we play that role after he died. That wish hasn't been respected," he said.

The foundation's executive director, Rina Hore, said she understood the family would like to have a say in how the trademarks were licensed.

"But we have to do it through consultation," she said.

Ms Hore said the legal right to the trademarks were given by Sir Donald to the foundation.

"[The foundation] is not in a position to give away the responsibility and the management of those to another party," she said.

Ms Hore acknowledged its licensing of Sir Donald's name had not always been ideal.

Not long after Sir Donald's death in 2001, the Bradman Foundation licensed the Bradman name to a biscuit company, Unibic, something Ms Hore said the foundation now regrets.

John Bradman said the family was not consulted about the licensing to Unibic.

"The foundation would never have dared license his name in that way without his consent while he was alive and he would not have expected them to do so without his family's consent after he died," Mr Bradman said.

''My father is a loved and missed family member and not as a brand name like Mickey Mouse.

Ms Hore admitted the decision was "certainly the catalyst for the family and the foundation to lose the working relationship they had".

"The foundation took a great lesson out of that in that we've ensured any licensing we've done from that day on has been cricket related," she said.

'Hall of Fame' decision deepens the divide

Nine years after Sir Donald died, the foundation drew on federal funding to become the International Cricket Hall of Fame.

"He wanted [the Bradman Museum] to be a small local entity," John Bradman said.

"And of course it is now greatly expanded in ways that he would not have supported."

But Ms Hore is adamant the right decision was made.

"We had to ensure that the museum was relevant, we had to ensure it could engage with new audiences and we were also in an era where the game of cricket was evolving at a rate that far exceeded anything in Sir Donald Bradman's time," she said.

"And we needed to ensure that we had global international content so that our visitors that came to this museum could see their own heroes."

Ms Hore said she was appointed after Sir Donald's death, and does not know what he would have wanted.

"I am not in a position to understand all of his wishes, I was not part of the family and I didn't meet Sir Donald Bradman," she said.

Nevertheless, she said he was "very insistent" the museum should never be allowed to fail.

"We don't expect others to necessarily feel the same way or feel as strongly as we do," Greta Bradman said.

"But if you can imagine a loved family member and having no control over their name or their likeness, and having it used in a way that you know would be profoundly not okay with that individual — it's just something that we can't live with."

John Bradman added: "There were so many times when I just wished my father would come back to life because in a sentence he could have fixed it."