A "familiar spirit" is a spirit that's well known or familiar to you

In modern English, "familiar" means well known or recognized, so "a familiar spirit" sounds like it describes a spirit somebody has a personal acquaintance with, maybe one that's attached itself to a person or family across generations. That is not what the KJV translators meant when they used the phrase in verses like 1 Samuel 28:7 and Leviticus 20:27.

The English word "familiar" here comes from the Latin familiaris, related to famulus, a household servant. The sense the Geneva and King James translators were reaching for is a spirit that attends or serves a medium the way a household servant attends a family, not a spirit the medium simply happens to know. The underlying Hebrew word behind it is 'ôb, the Old Testament's standing term for necromancy and mediumship, the same word behind the practice of the medium of Endor whom Saul consults in 1 Samuel 28, in direct violation of the prohibition given in Leviticus 20:27 and elsewhere. "Familiar spirit" was the Elizabethan translators' way of naming that necromantic, servant-like role, using a sense of the word "familiar" that has since died out of everyday English.

That dead sense is exactly the kind of gap that manufactures a modern myth by accident. Read with today's meaning of the word, "familiar spirit" sounds like it's describing generational or attaching spirits, and a fair amount of popular demonology about spirits that latch onto families has been built on exactly that misreading. None of it comes from the Hebrew text. It comes from four centuries of ordinary semantic drift in a single English adjective that nobody updated when the language moved on.