Well the 501st has the same problem. The difference is they were canonized after their formation, but still Lucas technically owns the name.
The thing is we exist by the good graces of Bungie and MS. As long as we represent them well and "use our powers for good" then we'll probably continue to exist.
If you are asking what legal recourse we have for people stealing our stuff, anything 405th (like the logo) that has no halo imagery on it whatsoever is ours (Adam's). You can't really copyright a number. There could be any number of works out there that have a ship or a planet or something named 117. The real problem is the Halo imagery which you notice the 405th does not have in the logo.
Battletech has an Irian Hussar's 405th Infantry Brigade (older than Halo by 15 years)
Real life has the 405th Air Expiditionary Wing, 405th Army Field Support Brigade, 405th Fighter Wing, and I'm sure there are others I'm missing.
But the reality of other people using our 405th logo on merch without permission is much more like the recourse we have for recasting. IP Ban said person, Blacklist said person, notify other prop sites of what they did. With that being their only market for such stuff they've pretty much shot themselves in the foot and ruined their chances at being able to work with people on future projects. Of course that is a worst case scenario. More than often it's just a misunderstanding of the rules that doesn't require we go that far.