The Tasmanian Aboriginal Council (TAC) put forward the name nipaluna - drawn from the revived Aboriginal language of palawa kani - at a ceremony on Wednesday as part of Reconciliation Week.
"It is about unveiling the true history of the area and letting people know that there were other people here before the English," TAC CEO Heather Sculthorpe said.
"That gives all Aboriginal people a pride in place of identity and ... knowing where they've come from.
"To say 'oh nipaluna, that's my language, I know that, that's my people' - it can't be overestimated, the worth of that."
She said it was documented during colonisation that Indigenous people told European settlers the Hobart area was called nipaluna.
Aboriginal leader Wooreddy shared the name with missionary George Augustus Robinson in January 1831.
"Later on in that same year ... Wooreddy gave more details that this was the name of this area and how people had watched ships come in," Ms Sculthorpe said.
Hobart City Council Mayor Ron Christie has pledged to use the name as often as possible and will take it to a council vote, one he expects it to pass.
"Whenever I'm attending a function or welcoming delegates to this city, I will be welcoming them to nipaluna, Hobart city," he said.
But the formal use of nipaluna, including on signs and maps, can't happen unless it is approved by Tasmania's Nomenclature Board.
A spokesperson for the government said it does not support a dual name for Hobart.
Several natural landmarks in the state have dual names, including kunanyi/Mount Wellington which was in 2014 formally given the Indigenous name under the government's Aboriginal dual naming policy.
The policy is being reviewed by the state government after concerns were raised over a lack of consultation in deciding names.
“(The government) is optimistic the TAC will contribute to the consultation to ensure their views are included in the review process," the spokesperson said.
Rodney Dillon, co-chair of Tasmanian Regional Aboriginal Communities Alliance (TRACA), accused the council of not consulting widely enough.
"I am very supportive of having Aboriginal names of places. But you have got to let all the groups have a say in it," he told the ABC.
Ms Sculthorpe hopes the council's support will lead to a groundswell of community support.
"I think there will be an overwhelming sense that the premier won't be able to ignore," Ms Sculthorpe said, adding decades of research went into finding the most accurate name.
"Let's give pride to the people whose language it is."
AAP - Ethan James