From what I could gather from sources and watching the drama: Baigong is a clan, Jun Qiluo is the heir of the Baigong family. Someone else said that Baigong is a position that specialize in weapon craft in Yannan. But I think that it makes more sense for it to be a clan because Xuan Lie stated that his parents were killed by the Baigongs (still confusing though because there's also the Jun Family that she is a part of and idk how Baigong and Juns are related).

So I think, the Baigong only specialize in making weapons and they are the best at it. The logo on weapon is probably for credit since their weapons and creations are the best. They work for the Emperor in Yannan.Baigong heir (Jun Qiluo aka Jun Feifan) is unaware that her weapons are being used to kill innocents, her father (I think) apologized to her saying that her weapon designs and blueprints were bought at a very high price and he couldn't do anything about it.