Hello, everyone! I just had a brainsurge and wrote something up that I think ought to be shared to see whether people feel it could be useful in their own games. I think that this may be mostly implied in canon depictions of Rokugan, but I think that having it stated is worthwhile, so people who miss implications (like myself) can add some more depth to their own Rokugans. As such, without further ado, let's get on with it, shall we?
Being a Minor Clan samurai sucks. You cannot really get around that - such a samurai is less prized by the rest of the Empire, their achievements ignored in favor of those of a Great Clan samurai, and they are often disrespected by many more people than would ever dare to disrespect someone from one of the Great Clans. Furthermore, sometimes when a Minor Clan samurai arrives at an important court, they realize that only one or two samurai there have even heard of their Clan!
The sad fact is that throughout most of the Empire's history (right up until the establishment of the Alliance of the Minor Clans), the overwhelming majority of the samurai of the Empire are only aware of a few Minor Clans at any one time. Most samurai will likely have heard of the Mantis, the Fox (both Clans which are noted for having hosted the Imperial Winter Court as Minor Clans, albeit only rarely), and maybe one or two other Clans.
For instance, the average Dragon or Phoenix samurai is likely aware of the Mantis, the Fox, and the Dragonfly, while the average Crane has heard cautionary tales of Doji Suzume and the Clan he founded. The Crab have some interaction with the Falcon, and may even remember the Badger, but the Badger exist in isolation for so long that that is often not the case. The Scorpion remember the Hare well, likely have clashed with Sparrow as well (due to their abutting borders), and (once they start existing) have a long-standing grudge with the Wasp. The average Lion knows of the Dragonfly, most likely, due to the humiliation that that Clan's existence is to the Clan of Akodo, but may not have heard of many others.
There are exceptions, of course. An Asako who focuses on chronicling the creation and destruction of Minor Clans would probably be able to name all such existing Clans with a reasonable amount of accuracy, and an Ikoma might have a precise memory about reading that X Clan was created in the Y year of the reign of the Z Emperor. Any samurai who has the misfortune of being sent to treat with the Dragon after the eighth century probably knows more about the Dragonfly than they ever wished to know, and someone who has had the luck to meet a Sparrow Storyteller can probably tell anyone about the Sparrow Clan in such detail that no one would ever be able to forget the experience... but for the most part, the Great Clan samurai simply don't care about the Minor Clans.
This, in turn, means that in many cases, unscrupulous (and incredibly unwise) ronin otokodate can call themselves a Minor Clan, claiming a given part of neutral territory as their “Imperially-granted” land. Such ronin are able, due to this general (willful) ignorance of Great Clan samurai, to leverage some level of respect from Clan samurai - at least, until they are discovered, at which point most Clan samurai are quite willing to step in and execute Imperial justice upon the lying wave-men. Nevertheless, this tactic is something that comes up repeatedly, because really, though living as a Minor Clan samurai sucks, living as a ronin sucks more. Besides, some even hold to the hope that the reigning Emperor or Empress will look upon them and legitimize their claim - something not canonically done outside of the Mantis during the reign of the Gozoku.
So there we go. This post's rather shorter than my last ramble about the stories that could be told with a given Clan, but there you go. Maybe it will help enhance your gaming experience to include these "False" Minor Clans, but it ought to be established beforehand that although your players may know which Minor Clans exist at a given time, their PCs do not. Otherwise it comes off feeling a bit forced, and you cannot really use the interesting and fun Hawk Clan Purist ronin path, which would be a shame.