I don't know of a simple technical name like cube. I think the most common name is rectangular box or just box.
In September 2006 we received this note.
So I know this might sound nit-picky but I had a question that wasn't resolved by your website and then found the answer somewhere else. The question was asked by Jack here about what a 3d rectangle would be called. Penny replied there wasn't any name aside from box. This is not correct. It is called a cuboid. Please post this or at least let Jack know. We wouldn't want websurfers at large thinking there is no such thing as a cuboid. (they even got the answer right on The Answerbank website.)
Thanks for sending us this note. I was not aware of this meaning of the word cuboid. I checked the Oxford English Dictionary and found that cuboid is both an adjective and a noun. As an adjective they have
A. adj. Resembling a cube; of a form approximating to that of a cube; cuboidal; spec. in cuboid bone (os cuboides), one of the bones of the foot, between the calcaneum and the fourth and fifth metatarsal bones.
This meaning I knew, but one of the meanings of cuboid as a noun is
N 3. Geom. A solid resembling a cube, with the rectangular faces not all equal; a rectangular parallelepiped.
They even give a reference to the first use of cuboid with this meaning.
1890 R. B. HAYWARD Elem. Solid Geom. 78 Cuboids..on the same base are to one another as their heights. Note. The need of some short word in the place of the polysyllabic "rectangular parallelepiped" has been long felt. I have coined the work "cuboid".
Thanks again for this,