This post, which is linked from the ARS article states a given birthdate, gender, and zip code can uniquely identify most Americans. So, while the parent should probably specify birthdate instead of age, a name is definitely not needed.
Ah, birthdate makes much more sense. My confusion stemmed from misreading the comment as "using these properties: [given age](?), [gender], [zip code]" instead of "given these properties: [age], [gender], [zip code]".
This post, which is linked from the ARS article states a given birthdate, gender, and zip code can uniquely identify most Americans. So, while the parent should probably specify birthdate instead of age, a name is definitely not needed.