Wolf or Wolfgang had been jokingly suggested as names during filming, as had Corban, after fellow contestant Corban Walls.
Ben, 30, said that if he had to name his child after a fellow contestant and the baby was a boy, the choice would have to be Corban.
"If all Corbans are as smart as Corban, then it would be a good name," he told the Herald on Sunday in October.
The Christchurch couple, who were married in 2012, achieved the lowest sale price in the show's live auction finale, $1.3 million, earning them just $10,000 profit. Winners Alex and Corban Walls gave $30,000 to the Alexandres after their home sold for more than $1.5m which, combined with their prize money meant a $307,000 profit.