Dipping an amethyst in a potion of booze will turn it into a potion of fruit juice. This is a good way to identify both the potions of booze and fruit juice and the amethyst, since no other gem transforms a potion by being dipped into it. Identifying fruit juice will also distinguish it from the see invisible, which has the same messages.
In slashem, an amethyst can be used in gem alchemy by dipping it in acid to produce a magenta potion.
The ancient Greeks believed that the stone protected its owner from drunkenness. The name comes from the Greek ἀ a- (“not”) and μέθυστος methustos (“drunk”). This is why it transforms booze into fruit juice in NetHack.