As a biologist, but not a physiologist, I’m a little nervous answering questions about the nervous system. But if I were a psychologist I might have the nerve to say that the problem lies in the question, rather than the answer.
The answer appears simple. “Nerve” is the noun, “nervous” is the (latinate) adjective.
But the question suggests that the poster is, well, nervous because in English the adjective can have two distinct meanings — 1. Related to the nerves; 2. agitated and apprehensive (Chambers).
However this is a little unfair to the poster as I think that there is a psycholinguistic justification for his question. ‘Nervous’ does not obviously sound latinate to the general public — unlike other anatomical adjectives such as cardiac, pulmonary, ocular, for which there are common English equivalents. And in the English equivalents the noun is used as an adjective (heart surgery, lung disease, eye trouble).
This possible mental confusion would not have existed at the time that ‘nervous’ entered the English language in the 1660s, when it did so in its anatomical sense, being derived from the Latin, nervus. It was only later (1740) that its alternative and more general use arose (according to Etymonline). Indeed the mental association that became possible after this time may have been the reason for the later (about 1830) introduction of the Greek adjective, neural, into medical and scientific English. This is the basis of more modern terminology, but ‘nervous system’ was presumably too well established to be displaced by ‘neural system’ — even neurologists wouldn’t have the nerve.