Alchemy has been much romanticized, and much superstition has sprung up around it. The reality of alchemy is that while the Dark Ages of science swept over Europe, leaving the populace ignorant at best, Eastern scholars in the modern day middle east were making great advances in their understanding of minerals and medicine. They discovered not only a number of elements, but isolated specific compounds as well. Their medicines (and medical practices, which included hygenic methods) were far in advance of those found in Europe, and their culture allowed for constant experimentation and research, while Europe stagnated. The general name for these sciences in the Arabic tongue was al-Khimeia.
When the Crusaders reached the Arabic lands and found them so advanced, they didn't spend all of their time looting, raping, killing, etc. Some saw value in what they saw and learned from it, and brought stories, documents and artifacts back to share with others. This led to a renewed scientific curiosity in Europe, centered on a science that already had a name, which was quickly mispronounced or contracted to become alchemy.
The primary purpose of alchemy was not, emphasizing Not, to discover the secret to eternal life or to make gold. These two topics were of interest, as they would be extremely lucrative, but the average alchemist was interested in studying how the world around him worked, and how to manipulate it, like most scientists. Unfortunately, European governments were terribly afraid that someone might actually succeed in making gold, and destabilize their economy. The Church hated the thought of men dabbling in God's realm as well, particularly where eternal life was concerned. As a result, Europe outlawed the practice of alchemy.
People being what they are, making alchemy illegal did not deter those who really had a passion for the field. Alchemists continued to work, but they had to do so in hiding. Surrounded by people with no understanding of science and much superstition, rumors about what alchemists did surfaced, grew, mutated and reqppeared in ever more horrific incarnations. The populace feared the secretive alchemists, and regarded them in the same vein as witches.
Over time, the political power of the Church lessened, science re-emerged as an acceptable practice, and alchemy became a bit of a fashion for the wealthy nobility. Some would make actual useful discoveries, and record their observations properly. Others would expound theories based more upon their imagination than any real data. At long last, one Robert Boyle had had enough of the foolishness of some of his cohorts. He decided to express his take on how science should be practiced, and wrote a treatise on the topic - "The Sceptical Chymist". In this work he said that theories should be based on actual, reproduceable and quantifiable measurements and experiments. More to the point though, he was the first to refer to a practioner of the science as a Chymist (chemist). The name stuck, and the new age of scientific study that is chemistry began.