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.