This is a wonderful name for Harry Potter’s antagonist at Hogwarts. It’s also a fine example of a characteronym, a name that gives an impression or feeling close to who it is attached to.
The origin of the name should be clear. Draco is Latin for dragon, ultimately from the ancient Greek drakōn, meaning serpent. Draco is also the name of a constellation of stars, and of the first lawgiver in ancient Athens, which is where we got the word draconian from. Which is of course perfect as the first name of a nasty child whose family has been in Slytherin House for generations, since the symbol of the house is a snake.
Malfoy requires a bit more teasing apart. Though I can’t be certain what went through J. K. Rowling’s mind as she created this last name, it seems very similar to “mal” and “foi”.
The first part, mal, should be easily recognized as meaning evil or bad. It shows up in English in words such as malevolent, malicious, or malign, and comes from the Latin adjective “malus” meaning evil or bad.
The second part “foy” is strongly associated with “foi”, which is French for faith and comes from the Latin fides, meaning trust, confidence, reliance, belief, or faith. This Latin word gives us in English faith, fidelity, and related words.
So these two parts combined result in “bad faith”, “evil belief”, or any other combination of the above meanings. In law, mala fide means in bad faith or with intent to deceive. In the Middle Ages there was the infamous Malleus Maleficarum, called "The Witch's Hammer" in English, which described witchcraft for the Inquisition. It was named baced on the Latin word maleficia, used to describe people who commit evil acts, and in withcraft anything from illness and death to anything bad.
Draco’s father is not surprisingly named Lucius. This is a man’s name that isn’t common anymore, but whose origins are also Latin. Lucius was a common Roman praenomen (similar to a first name), and originates from the word lux, meaning light. The female version of the name is Lucia, and by extension Lucille, Luz, and Lucy. The interesting association to bear in mind here is that Lucius is closely related to Lucifer, which in Latin means “bearer of light”, and also refers to the morning star, the planet Venus. It is of course one of the names of the Devil as well.
Draco’s mother is named Narcissa, again a suitable name. This is clearly the female version of the name Narcissus, from Greco-Roman mythology. Narcissus is the youth who fell in love with his reflection in a pond and starved to death there because of his fascination with his own face. The flowers that later grew on the spot where he died were named for him, and we know them as narcissus. The name Narcissus and his myth gave rise in English to words such as narcissism and in psychiatry, narcissistic personality disorder. But Narcissus itself comes from the ancient Greek narkissos, meaning “numbness” with reference from the narcotic effects of the plant. This Greek root also gives us the word narcotic in modern English. So Narcissa Malfoy comes across as very self-centered and self-absorbed, making her name quite apt.
The Malfoy family is well named if not well liked. Their names are not all there is to them. They speak in the arrogant tones of the self-important, using formal language to condescend, and insulting terms, such as “mudblood” and “muggleborn” to offend. But ultimately, as we learn in Deathly Hallows, they are a family, united in a love for each other that proves deadly to Voldemort.