Final answer:
The support cells that cling to neurons and anchor them to blood vessels in the CNS are called astrocytes. These cells play a pivotal role in maintaining the neuronal environment and forming the blood-brain barrier.
Step-by-step explanation:
The support cells in the CNS that cling to neurons and anchor them to blood vessels are called astrocytes. Astrocytes are a type of glial cell found abundantly within the central nervous system. Their roles include maintaining the chemical environment around neurons, assisting in the formation of the blood-brain barrier, and providing structural support. They interact with both neurons and blood vessels, playing a critical role in neuron function and protection.