Active touch information, or sensory information from one side of the body going to the opposite hemisphere, is often called:

The answer to this question is decussation.

In the central nervous system, the signal can be delivered to the same side or the opposite of the body/brain. When someone gets a stroke and can't move his left side of the body, the lesion probably on the right side of the brain.
The opposite side is generally called contralateral where the same side called ipsilateral.