They haven't as they were manufactured outside the Omicrons on a temporary shipyard by a subgroup that has specialists to do so, ex-APM.
I mean, one day someone will come by and wonder why those have other logos/labels but anyway the ships are legal produced by a company/group that is apart of the faction (BHG) where the ships officially belong to. And as there is no official BHG| faction anymore, or any active that could handle this we had to improvise.
Same goes for gaians, when writing To: Gaians ... you mean anyone that is having a group of that and not specially <G> or [G-]. One of both responds, no matter what. But when one of the groups offer a better price then the other becuz they are in house space, and Knight gets the goods so where is the problem?
Also the ZoI of Core is limited to Omegas/Omicrons they have to count on the BHG to find stolen ships and bring them back to the Core if "APM" builds all. But this isn't possible if there is no co-operation between both groups and core tries to claim all.
- BHG-> takes care of House
- Core-> Omegas/Omicrons
Both groups should somehow work together.
And a ship registry would be useful, yes. But I doubt that you need it with only those 2 shipyards you have there, you can count the ships you are producing there by hand, no problem. (welp no offence, but last time I mentioned that APM has only 2 Shipyards you ignored it or overread it)
