I have a J-327 like that. I got it way back when. It might have even been before that system was in. But It could have been also because it was a CP ship. However my Y-wing also doesn't have a DOM so I think it is because they are older.
Commodore, Sir Pepi Deto
Falleen Protection Forces CO
Dean, Ichigo Military Academy
Trade Federation Citizen L1
Some ships are just really old, its my guess its the ships that were first in Darkness from the old system, and ships made by admins, my modded gallo doesn't have DOM nor my 3 digit TIE/Ln. I remember there was talk about it some time ago and admins might have explained it better, but can't recall that.
They didn't add the DOM until the most recent iteration of Production. (I'm not sure if that was even added with Production or a bit later. I don't remember it from Production Beta but it has been a while.)
In summary: anything with a low enough ID will not have a DOM.
If by production beta you mean the earliest form of production that didn't use RMs yet, yeah those ships (and any ships dating back to pre-production) don't have DOMs. Roughly the 10000-90000 ID range is from the earlier production run; starting with the 100,000s in about Y7-8 the DOMs are recorded.