Is it possible to use Pentax K mount lenses on a Pentax 645 via an adapter? If so, what is the name and type of adaptor required?
No. Even, if someone would build an adapter it could not possibly fully work.
One normally adapts a lens for a larger format to a camera with a smaller format. Going the other way, as you suggest, would place a lens with a small imaging circle compared to your sensor or film and result in clipped edges. other words you would only the center which kind of negates the purpose of a larger format.
The other number to pay attention to is the flange distance. You can bridge a gap for a lens that requires a longer one but mounting it too far makes such lenses not able to focus past a few centimeters or less than a meter. This would happen if you placed a K-mount lens in front of a 645 mount camera.