The former leaders of Dubbo and Wellington councils should be involved in the merged entity, according to the Dubbo Ratepayers and Residents Association.
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Last week it was announced Dubbo City Council and Wellington Council would be amalgamated to form Western Plains Regional Council.
The mayor and 10 other councillors have been removed from their posts to be replaced with an administrator until an election in September 2017.
However, Ms Mulcahy said the mayors and deputy mayors of both councils should continue to have a role.
"I'm hoping that we'll have the deputys and mayors from Wellington and Dubbo as overseers- that would be good, that would be terrific, that would be a bit of a safeguard I guess," she said.
"Eighteen months is an awful long time to leave us completely unrepresented."
The new council is one of 19 created in NSW.
The NSW government has said the mergers could free up almost $2 billion over the next 20 years, allowing councils to fund better services and new infrastructure for communities or lower rates.
"I'm pretty devastated that it ended up like this but I think whatever happens we will have to make the best of things," Ms Mulcahy said.
"None of us are particularly thrilled about it but we've got to make sure it does work for us, all of us in the Western Plains."
While The Real Estate Institute of NSW - Orana has said the loss of 'Dubbo' from the name will affect the city's identity, Ms Mulcahy said she was unconcerned.
"I think the name is alright, I like the name. I'm glad it isn't something like the Dubbo Wellington Council," she said.
"I think that Western Plains gives us more of an expansive attitude, which is what we're doing, we're expanding and we're no longer just Dubbo."
The sentiment was echoed on the Daily Liberal Facebook page.
One commenter said: "Dubbo will always be Dubbo to me, and I'm sure most of the population".
Another said that Dubbo would remain as "Dubvegas" and its reputation could never change.