Though there is no official name for this pairing (but if there is, please tell me. D:), the one pairing name that would probably fit them is Protectiveshipping. Sure, the name looks funny when you look at it, but after reading Onisarashi-hen, it makes more sense.
In the beginning of the Onisarashi-hen, Akira is sort of distant from Natsumi, having his suspicions. But, he later tells Natsumi that he likes her a lot, giving her his love confession. However, Natsumi has yet to tell him that she likes him a lot also.
However, ever since the Great Gas Disaster in Himnamizawa, anyone from there or in that area was treated with discrimination, and poor Natsumi would be no exception if everyone found out that she was from Okinomiya. When she and Akira walk by her house and see these strange 'offerings' that were put up by her grandmother, Natsumi was afraid that Akira would think she was weird. However, Akira keeps the incident a secret and when he learns that she is, in fact, of Hinamizawan origin, he declared that gave him more of an incentive to protect Natsumi.
About This Fanclub~
I've always liked this pairing and decided recently to make a fanclub for it. And if you like Natsumi x Akira, welcome. ;3