The names Ollar Link, Ollar Pass and Six Mile Pass have been proposed by the developer for the road linking Templepatrick Road and Doagh Road.
The road which has been constructed by Lotus Homes currently accesses three new developments – Ollar Valley, Rushfield and Hansons Hall.
A report to the committee indicated that the developer is keen to retain the “connection” to the Sixmile River which was known originally as Ollar.
The deferral was proposed by Ballyclare DUP councillor Alderman Mandy Girvan and seconded by party colleague Dunsilly councillor Alderman Linda Clarke.
Ald Girvan said: “Over Christmas, we have not had time to meet as a DEA (District Electoral Area) to discuss the names. I do not know if the names the company have provided us with would meet with approval.”
Ald Clarke added: “I am happy to second the proposal.”
The first phase of Ballyclare’s long-awaited relief road was officially opened in December.
Lotus Homes pledged to deliver the first phase of the scheme, which runs for 800 metres, in 2019, when progressing plans for 209 new family homes in the town.
Speaking at the official opening, managing director Paul O’Rourke said: ”The Ballyclare Western Relief Road has been called for since the 1980s, and we are delighted to be able to deliver the first phase of this significant piece of infrastructure to benefit the people of Ballyclare.
“We are grateful to the elected representatives for their support during the construction of the road, as we know how strongly they have campaigned for this road to be built.
“Ballyclare has been identified as having a fast growing population due to its popularity and we are confident that our investment in Ballyclare’s infrastructure will not only improve travel for residents, but will also help to create commercial opportunities for the town.”
Meanwhile, Ballyclare Ulster Unionist Councillor Norrie Ramsay said in an online post that he has contacted the Department for Infrastructure to request that this route is included for gritting “as a priority”.
Michelle Weir, Local Democracy Reporter