The neuron processes that normally receive incoming stimuli, and surround the cell body, are called:

Dendrites
Dendrites are projections of a neuron that receive signals from other neurons through chemical signals and electric impulses (electrochemical signals). Dendrites are covered with synapses (gland cells over which nerve impulses pass) which help them integrate information from many other neurons. The dendrites usually receive the signal transfer through chemical signals and it then travels to the cell body (soma) of the neuron from which the dendrites project. Most neurons have several dendrites, which may branch many times and frequently extend over a large area.