Science is full of examples, from Hippocrates, the Greek medic born around 460 BC, who gave his name to the Hippocratic Oath still used by doctors today, to Robert Brown, the 19th century botanist who discovered Brownian motion.
In cases where most people know something of the life or work of the person in question, their adjective often takes on a broader meaning. Although Darwinian often simply means ‘as described or discovered by Charles Darwin’, it is also used more generally to describe a fierce competitive situation (in business, for example), in which the losers will be eliminated.
Many adjectives formed from authors’ names have also taken on a wider meaning based on characteristics of their works. For example, we use Kafkaesque (from Franz Kafka) to describe nightmarish, illogical situations, Orwellian (from George Orwell, particularly his novel 1984) for a state of constant surveillance and suppression of free thought, and Dickensian (from Charles Dickens) to describe scenes of poverty and squalor such as those depicted in his novels, in particular when we want to emphasize how inappropriate they are in the modern world.
Unusually among writers, Lord Byron’s adjective derives as much from his own life as from his poems. A Byronic character is brooding, lonely and romantic.
Politics is another area in which names often become adjectives, usually formed with the suffix –ist (Marxist, Stalinist, Maoist, etc) or –ite (Blairite, Reaganite, Thatcherite), while the political adjective Machiavellian (from Nicolò Machiavelli, who wrote about unscrupulous political practices in Renaissance Florence) has become so much a part of our language that it is often written without a capital letter.
All the adjectives mentioned so far come from family names, but of course those from monarchs use first names. The only ones in common use are Elizabethan (by which we mean Elizabeth I, not the current monarch), Victorian, Edwardian, and Georgian. While historians may talk about Williamite wars, the term is not in general use, and neither are Caroline (or Carolean), used for Charles I and II. It seems unlikely that the latter will be resurrected if and when Prince Charles becomes king, especially given that he is free to choose a different ‘regnal name’ on his coronation.