What is the name of this kind picture, a vertical cut of some object or terrain
It is a cross section. Merriam-Webster:
1a : a cutting or piece of something cut off at right angles to an axis also : a representation of such a cutting
...
3 : a composite representation typifying the constituents of a thing in their relations
Here is a cross section of the Earth from USGS. Notice that the section looks as if the Earth were sliced along a vertical axis:
