Anti-racism campaigner and Kullilli man Stephen Hagan said the name of the island was "about as offensive as you can get".

But a Lake Macquarie councillor said he did not "accept that First Nations people's offence takes precedence over the wider community".

The comments came after Lake Macquarie council voted on Monday to consult the community about renaming the controversial Swansea island.

The site is named after coal miner Herbert Greta Heaney who lived on the island and was nicknamed 'Coon' because he often had black dust on his face.

"When I saw the origin of the name I thought 'wow'," Dr Hagan said. "That's out and out racism. It's beyond all comprehension.

"First Nations people are called those names all the time. [Keeping the name] sends the message that you live in white Australia. It exemplifies racial intolerance.

"I'm just surprised it's still around and being debated."

That debate came to a head between councillors, who voted unanimously to commence consultation, including with the Local Aboriginal Land Council, to investigate alternate names for the island and Coon Island Point. Cr Jason Pauling supported the motion after asking for it to include consulting former island residents and Herbert Heaney's relatives, who he said expressed concern they hadn't been approached.

The Liberal councillor was vocal in criticising how the process had been handled, saying he didn't want it to be a "knee jerk reaction" to recent publicity.

"We talk about hurt, I have not known anything to be as divisive in our community as this issue," he said.

"It was private, council started speaking to the land council about this last year. Where has the hurt come from? Making this damn thing public."

But fellow Liberal councillor Kevin Baker, who put up the notice of motion, said he was approached by the media about the issue and had been working behind the scenes on it for many years.

"Unfortunately it hasn't progressed, unfortunately it came to a head when a certain brand of cheese was renamed," he said.

"This story was going ahead regardless.

"I would not allow that story to happen with it being a consensus that nobody cared because what message does that send to people in our community?

"This has been an issue for quite some time. Just because some people haven't heard of it doesn't mean it's not an issue, doesn't mean that people haven't been hurting."

Cr Pauling said he was personally indifferent to changing the name, but would only support a new name if the community wanted it.

"It's a matter for discussion," he said. "We can't pre-empt that.

"It's very easy to be offended. I don't accept that First Nations people's offence takes precedence over the wider community."

His comments were in stark contrast to Cr Baker, who said the current names were "not inclusive of all members of our society and should be relegated to the history books".

"We're not talking about Coon Cheese here, we're not talking about cancel culture, we're not talking about woke," Cr Baker said. "What is represented here is a genuine racist name.

"This brings severe hurt to some members of our community.

"What really upsets me is people marginalised in our community are getting horrible hateful comments said to them.

"I would like to recognise the hurt this has brought to some members of our community, I apologise for that hurt. It is important though that we have this conversation so we can hopefully move forward."

Bahtabah Local Aboriginal Land Council CEO Carol Proctor said she was pleased the community was being consulted over the matter.

"Obviously we want the name to change," Ms Proctor said. "We want to move on to something more positive.

"We're happy for it to go to community consultation and let it go through its course.

"If we can come to some sort name that suits everyone, that would be great.

"A dual name would be ideal but if that's not what the community wants that's fine."

Dr Hagan said he would like the name changed without consultation, but accepted there were processes the council had to follow. However, he said if the council decides not to proceed with renaming, he would appeal to Premier Gladys Berejiklian to change the name.