“Alchemy” is from the Greek khemeioa, which was either from Khemia, a name for Egypt meaning “land of black earth,” or the Greek khymatos “that which is poured out.” It was often used as a scientific term until the 1600s when “chemistry” arose from it, leaving “alchemy” with its more mystical sense.
The al- prefix predictably comes from the definite article (“the”) in Arabic, which appears to be the word’s second step on its journey to English. The Greek khemeioa is the first recorded instance of the term in a decree from the Roman emperor Diocletian against “the old writings of the Egyptians,” c. 300. This suggested that the original practice that would come to be called alchemy was detailed in these “old writings,” but perhaps had another name until Roman influence spread across Upper Egypt as Diocletian suppressed a regional uprising there and instituted Roman policies.
This supports the idea that the practice was so called because it was “of Khemia,” or the work of Egyptian (primarily Alexandrian) pharmaceutical chemists (though “pour” makes equal sense and may have had equal influence). Alexandria was, after all, very likely the birthplace of alchemical thought, which blended technology, religion, mythology, and philosophy into the study of the perfection of the human body, experimental metallurgy (e.g., transmuting baser metals into gold), the search for a universal solvent, general physical and chemical reactions, and the creation of a true panacea—such as a philosopher’s stone.
(Related: The word “elixir” was originally a Medieval Latin word for a philosopher’s stone, which, as you probably know, was thought to be able to cure diseases, prolong life, and turn baser metals into gold. It’s probably from the late Greek xerion “powder for drying wounds,” from xeros “dry.”)
Thereafter, the Arabic al-kimiya was used, which would give rise to the Medieval Latin alkimia, then the Old French alquemie—later alchimie, which would be adopted in English in the mid-14th century.
In the 1560s, the word chymist (later “chemist”) would arise as an English word for a scientific alchemist—dropping the Arabic prefix—and by the early 1600s “chemistry” would replace “alchemy” as a word for physical and chemical processes and the scientific study thereof, with “alchemy” retaining the mythical and philosophical concepts.