I am interested in the origin of the name. I am aware that Reil coined the term in the 1800s, but want to know why did he choose the term vegetative. I have not been able to find an answer to this question. Today it is called the autonomic nervous system.
"Vegetative" doesn't only mean related to plants, but has other less common meanings.
4 a (1) : growing or having the power of growing (2) : of, relating to, or engaged in nutritive and growth functions as contrasted with reproductive functions a vegetative nucleus b : promoting plant growth the vegetative properties of soil c : of, relating to, or involving propagation by nonsexual processes or methods Merriam-Webster
So the word "vegetative" refers to the growth/nutrition functions of the autonomic nervous system. The short answer is that he chose that word because, particularly at the time he chose it, that was an appropriate word to use to refer to the regulation of things like digestion. Since the autonomic nervous system has other functions, such as in sexual arousal, and because the term vegetative has other meanings, the term "autonomic" has completely replaced vegetative in this context.