are they named based on their functions?
Yes -  the right celebral hemisphere controls and processes signals from the left side of the body, while the left celebral hemisphere controls and processes signals from the right side of the body.
Cerebrum
The cerebrum is divided by the medial longitudinal fissure into two cerebral hemispheres, the right and the left. The cerebrum is contralaterally organized, i.e., the right hemisphere controls and processes signals from the left side of the body, while the left hemisphere controls and processes signals from the right side of the body. There is a strong but not complete bilateral symmetry between the hemispheres. The lateralization of brain function looks at the known and possible differences between the two.
where are cranial nerves 1 and 2 located In the cerebrum what is its anatomy? The cerebrum is the largest part of the brain; The cerebrum consists of two C-shaped cerebral hemispheres, separated  by a longitudinal fissure. what are its main function? It functions as the center of sensory perception, memory, thoughts and judgement; the cerebrum also functions as the center of voluntary motor activities. how are there named? The cerebral cortex, Cerebral hemispheres
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Cerebrum [SEP] Cerebral hemispheres
The cerebrum is divided by the medial longitudinal fissure into two cerebral hemispheres, the right and the left. The cerebrum is contralaterally organized, i.e., the right hemisphere controls and processes signals from the left side of the body, while the left hemisphere controls and processes signals from the right side of the body. There is a strong but not complete bilateral symmetry between the hemispheres. The lateralization of brain function looks at the known and possible differences between the two.