The history of squatter George Faithfull has come into new focus during the Black Lives Matter movement, with calls for his name to be removed from the street because he was involved in the killing of Aboriginal inhabitants in 1838.

A motion from Wangaratta mayor Dean Rees was supported unanimously at Tuesday's meeting, meaning council officers will conduct a consultation process with the city's Indigenous community to get their views on a possible name change.

But while councillors were happy to have the discussion, that does not mean they will support changing the Faithfull Street name.

Cr Harvey Benton said he would not support the move if it caused a divide in the city.

"I don't think it's right for us to judge history - history's there whether it's good or bad," he said.

"Whatever has happened in the past has happened.

"It doesn't matter if it's overseas or here, there's been terrible atrocities and there's been good things in history, but it's there and we can't alter it."

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Cr Ken Clarke said there was no evidence about the "supposed massacre" involving Faithfull, just "a lot of hearsay, a lot of letters written" and pointed out that 10 of the first 11 streets named in Wangaratta were after squatters.

"Whilst I have a very open mind about the issue, I spent some time over the past few days trying to get a picture of what really took place 162 years ago," he said.

"It's surprising that many of the stations were subjected to attacks and pilfering, including the Reverend Docker, but only Faithfull has been signalled out for change."

Only Cr Harry Bussell expressed sympathy to the push for a name change, saying the Black Lives Matter movement had prompted an evaluation of the dark side of history.

"There is some sympathy for those who want to see removed symbols by name and statue, which are silent about the ambiguities of history," he said.

"There's no doubt that George Faithfull is at best an ambiguous character.

"He is rightly recognised for the pioneering role he played in the establishment of European settlement in North East Victoria.

"Until recently, history has been relatively silent on his engagement with first Australians."

He said there were conflicting opinions in the community and although it might not result in changing the street name, he was pleased to see consultation with Wangaratta's Indigenous people had already started.

"Too often, we have dealt with issues concerning first Australians without permitting their voice to be heard," Cr Bussell said.

Cr Rees said no matter the outcome, it was important to acknowledge the truth.

"This could mean some storytelling or some significant plaquing or trails that explain the story fully," he said.

"Maybe changing the name may not be that process, but we'll wait and see what the recommendation comes back to council as and we'll decide from there."