Your ability to process language in the left hemisphere and spatial thinking in the right hemisphere is called:

Laterlization

Explanation:

Laterlization is defined as the tendency of the some neuron activity specially to one part of brain. The brain of human is broadly divided into hemisphere which is separated by longitudinal fissure and connected by corpus callosum.

As in the above given case one neuron activity that is process language are localized in left hemisphere while spatial thinking are localize in the right hemisphere