I'm almost certain the FoTC is a Materials Group that manufactures both weapons and armor for the Guardians. We've seen it on both armor and weapons, and we know it's not a faction, so I see no other reasonable theory.
As for the gun, I'm pretty sure it's been custom painted.
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I think FOTC is, as you stated, a manufacturer (similar to what we see in Borderlands). The other option I'm still considering is that it's could be something like the UNSC in Halo, which provides home-grown weapons and armor to the Guardians from within the City. Just a thought...
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I've been looking and I can't seem to find it. I may have it confused with the helmet we saw with the Seven Seraphs logo on it though. Either way, It's been on literally every in-engine weapon we've seen so far, which leads me to believe they're the manufacturer.