The hormone of fight or flight is named for its address. Adrenaline means, roughly, "the stuff from near the kidneys."
The adrenal glands sit right by the kidneys. Their name is Modern Latin, from ad-, "to, near," and renalis, "of the kidneys," from Latin renes, "kidneys." English recorded adrenal as an adjective in 1866 and "adrenal gland" in 1875.
In 1893 two researchers in England, the physician George Oliver and the physiologist Edward Schäfer, showed that the glands held a substance with dramatic effects on the body. The race to isolate it then crossed the Atlantic. From 1897 John Jacob Abel, in the United States, prepared crude extracts. By 1899 he had named the material "epinephrin," following a suggestion from the anatomist Josef Hyrtl. Hyrtl's term for the gland joined Greek epi, "upon," and nephros, "kidney."
Abel's product turned out to be the wrong substance. It was an inactive chemical derivative, not the hormone itself. In 1901 the Japanese chemist Jokichi Takamine, who had visited Abel's lab in Baltimore in 1900, prepared a pure extract of the active principle and patented it. Takamine coined adrenaline, adding the chemical suffix -ine to adrenal. The drug company Parke-Davis sold it under the trademark Adrenalin.
That left one hormone with two names that mean the same thing, one Latin and one Greek. In the United States, epinephrine became the generic name, on the mistaken assumption that Abel's extract and Takamine's were the same. It later became the international nonproprietary name as well. When the UK switched to those international names after a European directive in 1992, it made exactly one exception: adrenaline.
So an American doctor says epinephrine and a British one says adrenaline, and both are naming the kidneys. The everyday sense of the word came later still. The phrase "adrenaline rush" was in use by about 1970.