How many families constitue a Major Clan in Legend of the Five Rings

In Legend of the Five Rings, a list of families is presented for each Major Clan. There are some in the source book (usually 4 or 5 for each Clan), and some others in additional books.

However, does that mean that every samurai in a Major Clan belong to those families? Or does that mean that those families are the “big ones”, but they are several other families in the Clan?

i.e. can I make up a NPC last name at the top of my head without having to check the validity of the name?

I have read through all the lore information in Legends of the Five Rings 4th Edition core book, but could not find the answer to this.