After the Ministry of Arts Culture and Heritage confirmed that a name alteration of this nature did not require the approval of the Queen or the governor-general, Friends of the Opera House were consulted.
Of the members who responded, 74 per cent said they would support altering the name while 13 per cent said they were opposed and 8 per cent were neutral.
The council's customer experience group manager, Marianne Cavanagh, told the committee meeting the name change would not be costly.
"It will be cost-neutral," she said.
"The sign can easily be changed as part of the current repairs and maintenance."
The exterior of the Opera House is currently being painted and repaired at a cost of $140,000 and the work will be completed in mid-April.
Approval for the committee decision on the spelling alteration will be sought at the next full council meeting.