Indigenous leaders in South Australia's outback are pushing to return Lake Eyre to its original Aboriginal name.

The Arabuna people were granted native title over nearly 69,000 square kilometres of land in South Australia's north last week, including all of Lake Eyre.

The Federal Court decision gives them more say over what happens on their land.

Arabana chairman Aaron Stuart says he will begin a process to change the lake's name back to its traditional indigenous name, Kati Thanda.

He says it would be part of a healing process for his people.

"A name change back to the Arabana word would be the only rightful thing to do for the first people of that area," he said.

"For the Arabana people, it's part of a healing process which takes time, but it gives them more identity.

"To me, that's true reconciliation and I just hope that the rest of Australia will get behind this and support the name change."

The South Australian Government says there is a range of options including dual-naming rights, but the decision lies with the Geographical Names Board.