What is the name of the nerve that brings heart pain to the central nervous system?

There isn't just one: There may not be just one nerve that brings heart pain to the brain. This is why people describe their heart attack symptoms so differently. Some people get nausea, sweating and a sense of "just not feeling right, " while others get the more classic chest and arm pain. Others may get extreme heaviness in the chest and shortness of breath. Thi suggests that different nerve pathways can be involved.

Heart pain: The heart doesn't have pain fibers. The various symptoms associated with 'heart pain' come from lung, GI tract, skeletal muscle and other structures. As such there isn't just one pathway involved in cardiac symptoms.