I receive the question often, so I did some research into it. Here’s what I found.
Suncook is a census designated place (CDP). That means that when the government collects census data each year, they combine Allenstown and Pembroke, when collecting information. They do this because Suncook resembles a town, even though it doesn’t have its own government.
Allenstown is a town. That means that it is “a center of population.” It also means that unlike Suncook, it has a town government.
While I can’t substantiate this data, I believe that the post office uses Suncook because of its status as a CDP by the federal government, and the post office is regulated by the federal government.