Belonging to the Faction - sooner or later - is the mandatory requirement of this game. However, you may be a volunteer or you may have been forced to join. There are also ways out of the Faction, but it would make it difficult to continue adventuring with others.
Although it's well-known that Faction Paradox is organised as a family, there's some debate about why this might be the case. All the Great Houses are to some degree over-extended families (even if they don't generally reproduce through natural childbirth), but the Faction attaches far more importance to family titles than any of the other bloodlines. It's been noted that in this respect it's got something else in common with the voodoo-cults of the Caribbean, and as both voodoo and the Eleven-Day Empire have their roots on eighteenth-century Earth this might not be a coincidence. The way the vodoun describe the loa -spirits is remarkably similar to the way the Faction describes entities like the Grandfather of House Paradox, and indeed, for the vodoun the loa are often perceived as the founders of a spiritual “family”.
However, as with many of the voodoo-cults, Faction Paradox is a political organisation above all else. A cynic might point out that for all its ritual and technology, at heart the Faction's no different from any other cult- and the best way for a cult to ensure the loyalty of its members is to forge family ties between them. Furthermore, Faction Paradox is a House that's constantly preparing for war: the military wing might be relatively small, but it's notable that when a new member is indoctrinated into the “family” he or she is equipped with a weapon as part of the initiation process. So although the titles given to Faction agents might suggest family relationships, in practice they're closer to being positions in an army.
Each membership type in the Faction has one or more moves associated with it. When you choose that rank, you get the Starting Moves. You can also choose to instead replace the moves with ones from an earlier type (ie a Godparent could choose a Sombras Que Corta). Additional Moves are relevant to that rank and not a specific character playbook - when your character advances you may choose an Additional Move from your membership rank instead of a move in your character playbook.