For the first year of life, the newborn children are not given names. They are only referred to by their birth number. Only 50 children per year are born and taken care of in the nurturing center. That is where Jonas's father works. Each December the community has the Ceremony of One. That is when the nurturers announce the name of each one-year-old child to the community and announce to which family the child has been assigned.
The nurturers do not pick the names. In chapter 2 Jonas's father admitted that he took a peek at the list to know what Gabriel would be named. He must keep it a secret though, because it is against the rules to name a child before the naming ceremony.