The process in which brain connections which are repeated become covered and insulated with a layer of fat increasing the efficiency of the neural impulse is called

Myelination

Explanation:

Myelin is a fatty substance composed of lipids which surrounds the axons of the nerve cells in the central nervous system. The myelin is formed by the oligodendrocytes in CNS and Schwann cells in PNS.

The plasma membrane of the oligodendrocytes containing the myelin covers the axons of the neurons in spiral fashion thus proving a sheath around through the process called "myelination".

This myelin sheath protects the neurons from the external environment as well as insulates the neuron which increases the efficiency of the impulse.

Thus, Myelination is the correct answer.