Cab & chassis is the light duty truck term you're looking for, but you're not going to put a large box like that on a pickup.
Medium and heavy trucks that already have a box mounted are called "straight trucks"
For the sort of conversion you're wanting to do with the passthrough to the cab, you'll probably want to look for a truck that used to have a non-integrated sleeper, so you only need to worry about making a matching hole in the box. Bear in mind for your attic thoughts that a box on a heavy duty truck chassis is likely to already be at or near the 13'6" max height. I think those uhaul trucks are around 12'?
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