It seems to me that diffraction gratings are completely described by the double slit experiment-why then is it called a diffraction grating?
I don't think this is true, unless I'm incorrectly understanding what you mean by "are completely described by." I also don't understand what the double slit has to do with the rest of the question.
Interference is the mechanism that gives rise to the phenomenon of diffraction. Either name could have been used.
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They are two different phenomena.
Diffraction is what happens when waves encounter an obstacle, describing the way waves are distorted by the obstacle.
Interference is what happens when two sets of waves overlap.
It just so happens that in two slit diffraction, a wave becomes two sets of waves on the other side of the diffraction grating, allowing interference to occur. However the grating is not causing any interference directly - it is simply causing a single wave to become two waves which can then overlap. (it would be trivial but possible to keep the two waves separate on the far side of the grating so that diffraction occurred without interference)