As I mentioned in game; I like the idea of sub-groups within the game. Be it religious cults, different types of guilds, or crime syndicates like this!
Of course, any such RP must always adhere to the rules of the game, including area rules. Just because you’re a mafia gangster, it still doesn’t allow you to smoke a cigar inside Miranda’s, or to wave guns around in the park 
Later, when the game supports custom “character title tags” (or whatever I’ll call it) - tags that your character must be granted permission to use - they can be used to quickly identify other characters being part of the same syndicate/family, or perhaps a rivalling one. Eg. tags like thieves guild, la familia, or the sodality.